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Question

Prove the sum of cubes identity : $a cubed plus b cubed equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses$

hint Hint:

$left parenthesis a plus b right parenthesis left parenthesis c d right parenthesis equals a left parenthesis c d right parenthesis plus b left parenthesis c d right parenthesis$ where a, b, c and d are real numbers. We are asked to prove the given equation.

The correct answer is: Hence, the proof

Explanation:
The given equation is $a cubed plus b cubed equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses$ The LHS and RHS are a³ + b³
and $left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses$ respectively.
We have to prove they are equal. For that prove the LHS and the RHS are equal.
Step 2 of 2: Multiply the RHS in the given equation, $a cubed plus b cubed equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a cubed plus b cubed equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses end cell row cell a cubed plus b cubed equals a open parentheses a squared minus a b plus b squared close parentheses plus b open parentheses a squared minus a b plus b squared close parentheses end cell row cell a cubed plus b cubed equals a cubed minus a squared b plus a b squared plus a squared b minus a b squared plus b cubed end cell row cell a cubed plus b cubed equals a cubed plus b cubed end cell end table$
Hence, the proof.

To prove an equation to be equal, we have to prove either the RHS is equal to the LHS or vice versa. The side should be selected based on the simplification process.

How can you use polynomial identities to multiply expressions ?
$open parentheses 2 x squared plus y cubed close parentheses squared$

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Use polynomial identities to multiply the expressions ?
$left parenthesis x plus 6 right parenthesis squared$

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Use polynomial identities to multiply the expressions ?
$left parenthesis x minus 9 right parenthesis left parenthesis x minus 9 right parenthesis$

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Prove the polynomial identity $x to the power of 4 minus y to the power of 4 equals left parenthesis x minus y right parenthesis left parenthesis x plus y right parenthesis open parentheses x squared plus y squared close parentheses$

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Prove the difference of cubes identity :
$a cubed minus b cubed equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses$

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How could you use polynomial identities to factor the expression $x to the power of 6 minus y to the power of 6$ .

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Prove the sum of cubes identity :
$a cubed plus b cubed equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses$

Maths-General

General

Maths-

After diluting salt water, the concentration of salt in the water is given by the function $f left parenthesis x right parenthesis equals fraction numerator 0.5 x over denominator x squared minus 1 end fraction$ , where x is the time in hours since the dilution.
b. After how many hours will the concentration of salt in the water be ?Round to the nearest hundredth.

Maths-General

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Maths-

Which function has a graph with a vertical asymptote at x = 3? Select all that apply .

Maths-General

General

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Which function has a graph with a horizontal asymptote at y = -1.

Maths-General

General

Maths-

After diluting salt water, the concentration of salt in the water is given by the function $f left parenthesis x right parenthesis equals fraction numerator 0.5 x over denominator x squared minus 1 end fraction$ , where x is the time in hours since the dilution .
a. What is the concentration of salt in the water after 4 hours?

Maths-General

General

Maths-

A Software CD can be manufactured for $straight $ 0.10$ each. The development cost to produce the software is $straight $ 500 comma 000.$ . The first 200 CDs were used by testers to test the functionality of the software and were not sold.
a .Write a function f for the average cost , in dollars , of a sellable software CD , where x is the number of sellable software CDs
b. What are the vertical asymptotes of the graph ?
c. Graph the function

Maths-General

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Maths-

Amaya made 10 three point shots out of 25 attempts. If she then goes on to make consecutive three point shots, her success would be given by the function $f left parenthesis x right parenthesis equals fraction numerator x plus 10 over denominator x plus 25 end fraction$

Maths-General

General

Maths-

Which function has a graph with a horizontal asymptote at y = -1.
$text a. end text straight F left parenthesis straight x right parenthesis equals fraction numerator x plus 5 over denominator x minus 3 end fraction$

Maths-General

General

Maths-

Graph the function, labelling all horizontal or vertical asymptotes of the form x =a or y = b
$straight F left parenthesis straight x right parenthesis equals fraction numerator 6 x squared minus 12 x over denominator x squared plus 5 x minus 24 end fraction$

Maths-General

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Prove the sum of cubes identity :

where a, b, c and d are real numbers. We are asked to prove the given equation.

The correct answer is: Hence, the proof

Explanation:The given equation is The LHS and RHS are a3 + b3and respectively.We have to prove they are equal. For that prove the LHS and the RHS are equal.Step 2 of 2: Multiply the RHS in the given equation, Hence, the proof.

Related Questions to study

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After diluting salt water, the concentration of salt in the water is given by the function , where x is the time in hours since the dilution.b. After how many hours will the concentration of salt in the water be ?Round to the nearest hundredth.

After diluting salt water, the concentration of salt in the water is given by the function , where x is the time in hours since the dilution.b. After how many hours will the concentration of salt in the water be ?Round to the nearest hundredth.

Which function has a graph with a vertical asymptote at x = 3? Select all that apply .

Which function has a graph with a vertical asymptote at x = 3? Select all that apply .

Which function has a graph with a horizontal asymptote at y = -1.

Which function has a graph with a horizontal asymptote at y = -1.

After diluting salt water, the concentration of salt in the water is given by the function , where x is the time in hours since the dilution .a. What is the concentration of salt in the water after 4 hours?

After diluting salt water, the concentration of salt in the water is given by the function , where x is the time in hours since the dilution .a. What is the concentration of salt in the water after 4 hours?

Amaya made 10 three point shots out of 25 attempts. If she then goes on to make consecutive three point shots, her success would be given by the function

Amaya made 10 three point shots out of 25 attempts. If she then goes on to make consecutive three point shots, her success would be given by the function

Which function has a graph with a horizontal asymptote at y = -1.

Which function has a graph with a horizontal asymptote at y = -1.

Graph the function, labelling all horizontal or vertical asymptotes of the form x =a or y = b

Graph the function, labelling all horizontal or vertical asymptotes of the form x =a or y = b

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Prove the sum of cubes identity : $a cubed plus b cubed equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses$

$left parenthesis a plus b right parenthesis left parenthesis c d right parenthesis equals a left parenthesis c d right parenthesis plus b left parenthesis c d right parenthesis$ where a, b, c and d are real numbers. We are asked to prove the given equation.

How can you use polynomial identities to multiply expressions ?
$open parentheses 2 x squared plus y cubed close parentheses squared$

How can you use polynomial identities to multiply expressions ?
$open parentheses 2 x squared plus y cubed close parentheses squared$

Use polynomial identities to multiply the expressions ?
$left parenthesis x plus 6 right parenthesis squared$

Use polynomial identities to multiply the expressions ?
$left parenthesis x plus 6 right parenthesis squared$

Use polynomial identities to multiply the expressions ?
$left parenthesis x minus 9 right parenthesis left parenthesis x minus 9 right parenthesis$

Use polynomial identities to multiply the expressions ?
$left parenthesis x minus 9 right parenthesis left parenthesis x minus 9 right parenthesis$

Prove the polynomial identity $x to the power of 4 minus y to the power of 4 equals left parenthesis x minus y right parenthesis left parenthesis x plus y right parenthesis open parentheses x squared plus y squared close parentheses$

Prove the polynomial identity $x to the power of 4 minus y to the power of 4 equals left parenthesis x minus y right parenthesis left parenthesis x plus y right parenthesis open parentheses x squared plus y squared close parentheses$

Prove the difference of cubes identity :
$a cubed minus b cubed equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses$

Prove the difference of cubes identity :
$a cubed minus b cubed equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses$

How could you use polynomial identities to factor the expression $x to the power of 6 minus y to the power of 6$ .

How could you use polynomial identities to factor the expression $x to the power of 6 minus y to the power of 6$ .

Prove the sum of cubes identity :
$a cubed plus b cubed equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses$

Prove the sum of cubes identity :
$a cubed plus b cubed equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses$

Amaya made 10 three point shots out of 25 attempts. If she then goes on to make consecutive three point shots, her success would be given by the function $f left parenthesis x right parenthesis equals fraction numerator x plus 10 over denominator x plus 25 end fraction$

Amaya made 10 three point shots out of 25 attempts. If she then goes on to make consecutive three point shots, her success would be given by the function $f left parenthesis x right parenthesis equals fraction numerator x plus 10 over denominator x plus 25 end fraction$

Which function has a graph with a horizontal asymptote at y = -1.
$text a. end text straight F left parenthesis straight x right parenthesis equals fraction numerator x plus 5 over denominator x minus 3 end fraction$

Which function has a graph with a horizontal asymptote at y = -1.
$text a. end text straight F left parenthesis straight x right parenthesis equals fraction numerator x plus 5 over denominator x minus 3 end fraction$

Graph the function, labelling all horizontal or vertical asymptotes of the form x =a or y = b
$straight F left parenthesis straight x right parenthesis equals fraction numerator 6 x squared minus 12 x over denominator x squared plus 5 x minus 24 end fraction$

Graph the function, labelling all horizontal or vertical asymptotes of the form x =a or y = b
$straight F left parenthesis straight x right parenthesis equals fraction numerator 6 x squared minus 12 x over denominator x squared plus 5 x minus 24 end fraction$