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Maths-

General

Easy

Question

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

The correct answer is: There are some basic polynomial identities that you need to by heart.

$left parenthesis straight x minus straight a right parenthesis squared equals straight x squared minus 2 ax plus straight a squared$ , where x and a can be real values, variables or multiples of both.
We are asked to use identities to multiply the given expression.
Step 1 of 2:
The given expression is $left parenthesis x minus 9 right parenthesis left parenthesis x minus 9 right parenthesis$ . It can be written as:
$left parenthesis straight x minus 9 right parenthesis left parenthesis straight x minus 9 right parenthesis equals left parenthesis straight x minus 9 right parenthesis squared$ . It is of the form $left parenthesis x minus a right parenthesis squared$ .
Step 2 of 2:
Apply the identity $left parenthesis straight x minus straight a right parenthesis squared equals straight x squared minus 2 ax plus straight a squared$ to get the product of the expression:
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell left parenthesis x minus 9 right parenthesis left parenthesis x minus 9 right parenthesis equals left parenthesis x minus 9 right parenthesis squared end cell row cell equals x squared minus 2 left parenthesis x right parenthesis left parenthesis 9 right parenthesis plus 9 squared space space space space space space space end cell row cell equals x squared minus 18 x plus 81 space space space space space space space space space space space end cell end table$
Note:
We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.

Related Questions to study

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 $x to the power of 6 minus y to the power of 6$ .

parallel

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 :
$a cubed plus b cubed equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses$

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.

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.

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 .

parallel

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

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?

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

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

parallel

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
$straight F left parenthesis straight x right parenthesis equals fraction numerator 6 x squared minus 12 x over denominator x squared plus 5 x minus 24 end fraction$

parallel

Graph the function, labelling all horizontal or vertical asymptotes of the form x = a or y = b
$F left parenthesis x right parenthesis equals fraction numerator x squared plus x minus 2 over denominator 2 x squared minus 9 x minus 18 end fraction$

Graph the function, labelling all horizontal or vertical asymptotes of the form x = a or y = b
$F left parenthesis x right parenthesis equals fraction numerator x squared plus x minus 2 over denominator 2 x squared minus 9 x minus 18 end fraction$

Graph the function, labelling all horizontal or vertical asymptotes of the form x = a or y = b
$straight F left parenthesis straight x right parenthesis equals fraction numerator 2 x minus 1 over denominator x squared minus 3 x minus 10 end fraction$

Graph the function, labelling all horizontal or vertical asymptotes of the form x = a or y = b
$straight F left parenthesis straight x right parenthesis equals fraction numerator 2 x minus 1 over denominator x squared minus 3 x minus 10 end fraction$

Graph the function
$fraction numerator 3 x over denominator x minus 1 end fraction$

Graph the function
$fraction numerator 3 x over denominator x minus 1 end fraction$

parallel

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