Maths-

General

Easy

Question

Use polynomial identities to factor each polynomial :
$m to the power of 9 plus 27 n to the power of 6$

The correct answer is: The factor of the expression is, .

ANSWER:
Hint:
$a cubed plus b cubed equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses$ where a and b can be real values, variables or multiples of both.
We are asked to use polynomial identities to factor the given polynomial.
Step 1 of 2:
The given expression is $m to the power of 9 plus 27 n to the power of 6$ . It can be written as $open parentheses m cubed close parentheses cubed plus open parentheses 3 n squared close parentheses cubed$ . This is of the form $a cubed plus b cubed$ where $a equals m cubed straight & b equals 3 n squared$ .
Step 2 of 2:
Substitute the values in the expansion to get the factor form. Thus, we get:
$m to the power of 9 plus 27 n to the power of 6 equals open parentheses m cubed close parentheses cubed plus open parentheses 3 n squared close parentheses cubed$
$equals open parentheses m cubed plus 3 n squared close parentheses open parentheses open parentheses m cubed close parentheses squared minus open parentheses m cubed close parentheses open parentheses 3 n squared close parentheses plus open parentheses 3 n squared close parentheses squared close parentheses$
$equals open parentheses m cubed plus 3 n squared close parentheses open parentheses m to the power of 6 minus 3 m cubed n squared plus 9 n to the power of 4 close parentheses$
The factor of the expression is, $m to the power of 9 plus 27 n to the power of 6 equals open parentheses m cubed plus 3 n squared close parentheses open parentheses m to the power of 6 minus 3 m cubed n squared plus 9 n to the power of 4 close parentheses$ .
Note:
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.

Use the binomial theorem to expand the expressions:
$left parenthesis 3 x minus 0.2 right parenthesis cubed$

Maths-General

General

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Use polynomial identities to factor each polynomial :
$open parentheses 8 x to the power of 6 minus y cubed close parentheses$

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Maths-

Use the binomial theorem to expand the expressions:
$left parenthesis n plus 5 right parenthesis to the power of 5$

Maths-General

General

Maths-

Use polynomial identities to factor each polynomial :
$open parentheses 36 a squared minus 4 b squared close parentheses$

Maths-General

General

Maths-

Use the binomial theorem to expand the expressions:
$left parenthesis 2 m plus 2 n right parenthesis to the power of 6$

Maths-General

General

Maths-

Use polynomial identities to multiply each expression $open parentheses x plus 3 y cubed close parentheses squared$ .

Maths-General

General

Maths-

Use the binomial theorem to expand the expressions:
$left parenthesis d minus 3 right parenthesis to the power of 4$

Maths-General

General

Maths-

Use the binomial theorem to expand the expressions:
$open parentheses x cubed plus y squared close parentheses to the power of 6$

Maths-General

General

Maths-

Use the binomial theorem to expand the expressions:
$open parentheses 2 x plus 1 third close parentheses cubed$

Maths-General

General

Maths-

Use the binomial theorem to expand the expressions:
$open parentheses x squared plus 1 close parentheses to the power of 4$

Maths-General

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Use polynomial identities to multiply each expression .
$left parenthesis 2 x plus 8 y right parenthesis left parenthesis 2 x minus 8 y right parenthesis$

Maths-General

General

Maths-

Use the binomial theorem to expand the expressions:
$left parenthesis b minus 0.5 right parenthesis to the power of 4$

Maths-General

General

Maths-

Use the binomial theorem to expand the expressions:
$left parenthesis 2 a minus b right parenthesis to the power of 5$

Maths-General

General

Maths-

Use the binomial theorem to expand the expressions:
$left parenthesis x plus 3 right parenthesis cubed$

Maths-General

General

Maths-

Use polynomial identities to factor each polynomial : $m to the power of 9 plus 27 n to the power of 6$

Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.

Use polynomial identities to factor each polynomial : $m to the power of 9 plus 27 n to the power of 6$

Maths-General

Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.

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Use polynomial identities to factor each polynomial :

The correct answer is: The factor of the expression is, .

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Use polynomial identities to factor each polynomial :
$m to the power of 9 plus 27 n to the power of 6$

Use the binomial theorem to expand the expressions:
$left parenthesis 3 x minus 0.2 right parenthesis cubed$

Use the binomial theorem to expand the expressions:
$left parenthesis 3 x minus 0.2 right parenthesis cubed$

Use polynomial identities to factor each polynomial :
$open parentheses 8 x to the power of 6 minus y cubed close parentheses$

Use polynomial identities to factor each polynomial :
$open parentheses 8 x to the power of 6 minus y cubed close parentheses$

Use the binomial theorem to expand the expressions:
$left parenthesis n plus 5 right parenthesis to the power of 5$

Use the binomial theorem to expand the expressions:
$left parenthesis n plus 5 right parenthesis to the power of 5$

Use polynomial identities to factor each polynomial :
$open parentheses 36 a squared minus 4 b squared close parentheses$

Use polynomial identities to factor each polynomial :
$open parentheses 36 a squared minus 4 b squared close parentheses$

Use the binomial theorem to expand the expressions:
$left parenthesis 2 m plus 2 n right parenthesis to the power of 6$

Use the binomial theorem to expand the expressions:
$left parenthesis 2 m plus 2 n right parenthesis to the power of 6$

Use polynomial identities to multiply each expression $open parentheses x plus 3 y cubed close parentheses squared$ .

Use polynomial identities to multiply each expression $open parentheses x plus 3 y cubed close parentheses squared$ .

Use the binomial theorem to expand the expressions:
$left parenthesis d minus 3 right parenthesis to the power of 4$

Use the binomial theorem to expand the expressions:
$left parenthesis d minus 3 right parenthesis to the power of 4$

Use the binomial theorem to expand the expressions:
$open parentheses x cubed plus y squared close parentheses to the power of 6$

Use the binomial theorem to expand the expressions:
$open parentheses x cubed plus y squared close parentheses to the power of 6$

Use the binomial theorem to expand the expressions:
$open parentheses 2 x plus 1 third close parentheses cubed$

Use the binomial theorem to expand the expressions:
$open parentheses 2 x plus 1 third close parentheses cubed$

Use the binomial theorem to expand the expressions:
$open parentheses x squared plus 1 close parentheses to the power of 4$

Use the binomial theorem to expand the expressions:
$open parentheses x squared plus 1 close parentheses to the power of 4$

Use polynomial identities to multiply each expression .
$left parenthesis 2 x plus 8 y right parenthesis left parenthesis 2 x minus 8 y right parenthesis$

Use polynomial identities to multiply each expression .
$left parenthesis 2 x plus 8 y right parenthesis left parenthesis 2 x minus 8 y right parenthesis$

Use the binomial theorem to expand the expressions:
$left parenthesis b minus 0.5 right parenthesis to the power of 4$

Use the binomial theorem to expand the expressions:
$left parenthesis b minus 0.5 right parenthesis to the power of 4$

Use the binomial theorem to expand the expressions:
$left parenthesis 2 a minus b right parenthesis to the power of 5$

Use the binomial theorem to expand the expressions:
$left parenthesis 2 a minus b right parenthesis to the power of 5$

Use the binomial theorem to expand the expressions:
$left parenthesis x plus 3 right parenthesis cubed$

Use the binomial theorem to expand the expressions:
$left parenthesis x plus 3 right parenthesis cubed$

Use polynomial identities to factor each polynomial : $m to the power of 9 plus 27 n to the power of 6$

Use polynomial identities to factor each polynomial : $m to the power of 9 plus 27 n to the power of 6$