Maths-
General
Easy

Question

Use polynomial identities to factor the polynomials or simplify the expressions :
x cubed minus 27 y cubed

The correct answer is: The factor of the expression is x^3 - 27y^3 = (x - 3y)(x^2 + 3xy + 9y^2)


    ANSWER:
    Hint:
    open parentheses straight a cubed minus straight b cubed close parentheses equals left parenthesis straight a minus straight b right parenthesis open parentheses straight a squared plus ab plus straight b squared close parentheses, here a and b can be real values, variables or multiples of both.
    We are asked to use polynomial identities to factorize the given expression.
    Step 1 of 2:
    The given expression is x cubed minus 27 y cubed.text  It can be written as  end text left parenthesis x right parenthesis cubed minus left parenthesis 3 y right parenthesis cubed text . It is of the form  end text a cubed minus b cubed text  where  end text a equals x straight & b equals 3 y text .  end text
    Step 2 of 2:
    Use polynomial identities to simplify the given 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 x cubed minus 27 y cubed equals left parenthesis x right parenthesis cubed minus left parenthesis 3 y right parenthesis cubed space space space space space space space space space space space end cell row cell equals left parenthesis x minus 3 y right parenthesis open parentheses x squared plus left parenthesis x right parenthesis left parenthesis 3 y right parenthesis plus left parenthesis 3 y right parenthesis squared close parentheses end cell row cell equals left parenthesis x minus 3 y right parenthesis open parentheses x squared plus 3 x y plus 9 y squared close parentheses space space space space space space space space end cell end table
    The factor of the expression is straight x cubed minus 27 straight y cubed equals left parenthesis straight x minus 3 straight y right parenthesis open parentheses straight x squared plus 3 xy plus 9 straight y squared close parentheses
    Note:
    The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants.

    Related Questions to study

    General
    Maths-

    Use Pascal triangle to expandleft parenthesis x plus y right parenthesis to the power of 6

    Use Pascal triangle to expandleft parenthesis x plus y right parenthesis to the power of 6

    Maths-General
    General
    Maths-

    Use binomial theorem to expand (s2 + 3)5

    For the expansion of an expression (x + y)n , we would have n+1 terms. This is something you need to keep in mind.

    Use binomial theorem to expand (s2 + 3)5

    Maths-General

    For the expansion of an expression (x + y)n , we would have n+1 terms. This is something you need to keep in mind.

    General
    Maths-

    Use polynomial identities to factor the polynomials or simplify the expressions :
    8 x cubed plus y to the power of 9

    Use polynomial identities to factor the polynomials or simplify the expressions :
    8 x cubed plus y to the power of 9

    Maths-General
    parallel
    General
    Maths-

    Use Pascal triangle to expand left parenthesis x plus y right parenthesis to the power of 6

    Use Pascal triangle to expand left parenthesis x plus y right parenthesis to the power of 6

    Maths-General
    General
    Maths-

    Use polynomial identities to factor the polynomials or simplify the expressions :
    x to the power of 9 minus 8

    Use polynomial identities to factor the polynomials or simplify the expressions :
    x to the power of 9 minus 8

    Maths-General
    General
    Maths-

    Use Pascal triangle to expandleft parenthesis x plus y right parenthesis to the power of 5

    Use Pascal triangle to expandleft parenthesis x plus y right parenthesis to the power of 5

    Maths-General
    parallel
    General
    Maths-

    Use binomial theorem to expand (x - 3)4

    For the expansion of an expression (x + y) , we would have n+1 terms. This is something you need to keep in mind.

    Use binomial theorem to expand (x - 3)4

    Maths-General

    For the expansion of an expression (x + y) , we would have n+1 terms. This is something you need to keep in mind.

    General
    Maths-

    Use polynomial identities to factor the polynomials or simplify the expressions :
    x to the power of 8 minus 9

    Use polynomial identities to factor the polynomials or simplify the expressions :
    x to the power of 8 minus 9

    Maths-General
    General
    Maths-

    How is left parenthesis x plus y right parenthesis to the power of n obtained from left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent

    How is left parenthesis x plus y right parenthesis to the power of n obtained from left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent

    Maths-General
    parallel
    General
    Maths-

    Use Pascal triangle to expand (x + y)6

    The expansion of the polynomial (x + y)6  can be found using the values of 6Cr

    Use Pascal triangle to expand (x + y)6

    Maths-General

    The expansion of the polynomial (x + y)6  can be found using the values of 6Cr

    General
    Maths-

    Use polynomial identities to multiply the expressions ?
    open parentheses 25 straight x squared minus 15 straight y squared close parentheses open parentheses 25 straight x squared plus 15 straight y squared close parentheses

    Use polynomial identities to multiply the expressions ?
    open parentheses 25 straight x squared minus 15 straight y squared close parentheses open parentheses 25 straight x squared plus 15 straight y squared close parentheses

    Maths-General
    General
    Maths-

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
    12 cubed plus 2 cubed

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
    12 cubed plus 2 cubed

    Maths-General
    parallel
    General
    Maths-

    Use Pascal triangle to expand left parenthesis x plus y right parenthesis to the power of 5

    The answer cam also be found by expanding the formula of 5Cr .

    Use Pascal triangle to expand left parenthesis x plus y right parenthesis to the power of 5

    Maths-General

    The answer cam also be found by expanding the formula of 5Cr .

    General
    Maths-

    Use polynomial identities to multiply the expressions ?
    open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses

    Use polynomial identities to multiply the expressions ?
    open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses

    Maths-General
    General
    Maths-

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
    27 x to the power of 9 minus 343 y to the power of 6

    How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
    27 x to the power of 9 minus 343 y to the power of 6

    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.