Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

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

The correct answer is: Thus, the proof.

ANSWER:
Hint:
$open parentheses straight a squared minus straight b squared close parentheses equals left parenthesis straight a minus straight b right parenthesis left parenthesis straight a plus straight b right parenthesis$ where a and b can be real numbers, variables or multiples of both.
We are asked to prove the given equation.
Step 1 of 2:
$text The given expression is end text x to the power of 4 minus y to the power of 4 text . It can be written as, end text open parentheses x squared close parentheses squared minus open parentheses y squared close parentheses squared text . Applying the identity, we get: end text$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x to the power of 4 minus y to the power of 4 equals open parentheses x squared close parentheses squared minus open parentheses y squared close parentheses squared end cell row cell equals open parentheses x squared minus y squared close parentheses open parentheses x squared plus y squared close parentheses end cell end table$
Step 2 of 2:
Further application of the identity $open parentheses straight x squared close parentheses squared minus open parentheses straight y squared close parentheses squared equals open parentheses straight x squared minus straight y squared close parentheses open parentheses straight x squared plus straight y squared close parentheses$ is possible. Hence, we get:
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x to the power of 4 minus y to the power of 4 equals open parentheses x squared close parentheses squared minus open parentheses y squared close parentheses squared space space space space space space space space space end cell row cell space space space space space space space space equals open parentheses x squared minus y squared close parentheses open parentheses x squared plus y squared close parentheses space space space space space space space space space end cell row cell equals left parenthesis x minus y right parenthesis left parenthesis x plus y right parenthesis open parentheses x squared plus y squared close parentheses space space space end cell end table$
Thus, the proof.
Note:
We can use multiple identities to factorize an expression. Our aim is to reduce the expression into the lowest form.

Related Questions to study

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

parallel

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 .

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

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

parallel

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

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 $f left parenthesis x right parenthesis equals fraction numerator x plus 10 over denominator x plus 25 end fraction$

parallel

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

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
$F left parenthesis x right parenthesis equals fraction numerator x squared plus x minus 2 over denominator 2 x squared minus 9 x minus 18 end fraction$

parallel

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
$fraction numerator 3 x over denominator x minus 1 end fraction$

Graph the function, labelling all horizontal or vertical asymptotes of the form x = a or y = b
$F left parenthesis x right parenthesis equals fraction numerator x plus 4 over denominator 2 x squared minus 13 x minus 7 end fraction$

Graph the function, labelling all horizontal or vertical asymptotes of the form x = a or y = b
$F left parenthesis x right parenthesis equals fraction numerator x plus 4 over denominator 2 x squared minus 13 x minus 7 end fraction$

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.