Maths-
General
Easy

Question

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

The correct answer is: Thus, the expansion is: .


    Hint:
    Let a and b be variables or real numbers, then:left parenthesis a plus b right parenthesis squared equals a squared plus a b plus b squared
    We are asked to explain how you can use the polynomial identities to multiply expressions.
    Step 1 of 2:
    Here, the given expression isopen parentheses 2 x squared plus y cubed close parentheses squared , where .a equals 2 x squared straight & b equals y cubed
    So, we can use the identity left parenthesis a plus b right parenthesis squared equals a squared plus a b plus b squaredto find the expansion of open parentheses 2 x squared plus y cubed close parentheses squared .
    Step 2 of 2:
    Apply the polynomial identity, left parenthesis a plus b right parenthesis squared equals a squared plus a b plus b squared to get the answer of open parentheses 2 x squared plus y cubed close parentheses squared Thus, we have:open parentheses 2 x squared plus y cubed close parentheses squared equals open parentheses 2 x squared close parentheses squared plus 2 cross times 2 x squared cross times y cubed plus open parentheses y cubed close parentheses squared
    equals 4 x to the power of 4 plus 4 x squared y cubed plus y to the power of 6
    Thus, the expansion is: 4 x to the power of 4 plus 4 x squared y cubed plus y to the power of 6
    Note:
    Any expression of the form  left parenthesis a plus b right parenthesis squaredcan be expanded using the identity left parenthesis a plus b right parenthesis squared equals a squared plus a b plus b squaredrather than using the conventional and time taking method of multiplying them,left parenthesis a plus b right parenthesis left parenthesis a plus b right parenthesis .

    Related Questions to study

    General
    Maths-

    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

    Maths-General
    General
    Maths-

    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

    Maths-General
    General
    Maths-

    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

    Maths-General
    parallel
    General
    Maths-

    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

    Maths-General
    General
    Maths-

    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 .

    Maths-General
    General
    Maths-

    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

    Maths-General
    parallel
    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.

    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
    General
    Maths-

    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 .

    Maths-General
    General
    Maths-

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

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

    Maths-General
    parallel
    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?

    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

    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
    General
    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 functionf 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 functionf left parenthesis x right parenthesis equals fraction numerator x plus 10 over denominator x plus 25 end fraction

    Maths-General
    parallel
    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

    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

    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
    General
    Maths-

    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

    Maths-General
    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.