MATHEMATICS HIGH SCHOOL

Which expression is a difference of cubes? 9w^33-y^12 18p^15-q^21 36a^22-b^16 64c^15- a^26

Answers

Answer 1

Answer:

we know that

A polynomial in the form $a^(3)-b^(3)$ is called adifference of cubes. Both terms must be a perfect cubes

Let's verify each case to determine the solution to the problem

case A) $9w^(33) -y^(12)$

we know that

$9=3^(2)$ ------> the term is not a perfect cube

$w^(33)=(w^(11))^(3)$ ------> the term is a perfect cube

$y^(12)=(y^(4))^(3)$ ------> the term is a perfect cube

therefore

The expression $9w^(33) -y^(12)$ is not a difference of cubes because the term $9$ is not a perfect cube

case B) $18p^(15) -q^(21)$

we know that

$18=2*3^(2)$ ------> the term is not a perfect cube

$p^(15)=(p^(5))^(3)$ ------> the term is a perfect cube

$q^(21)=(q^(7))^(3)$ ------> the term is a perfect cube

therefore

The expression $18p^(15) -q^(21)$ is not a difference of cubes because the term $18$ is not a perfect cube

case C) $36a^(22) -b^(16)$

we know that

$36=2^(2)*3^(2)$ ------> the term is not a perfect cube

$a^(22)$ ------> the term is not a perfect cube

$b^(16)$ ------> the term is not a perfect cube

therefore

The expression $36a^(22) -b^(16)$ is not a difference of cubes because all terms are not perfect cubes

case D) $64c^(15) -a^(26)$

we know that

$64=2^(6)=(2^(2))^(3)$ ------> the term is a perfect cube

$c^(15)=(c^(5))^(3)$ ------> the term is a perfect cube

$a^(26)$ ------> the term is not a perfect cube

therefore

The expression $64c^(15) -a^(26)$ is not a difference of cubes because the term $a^(26)$ is not a perfect cube

I'm adding a new case so I can better explain the problem

case E) $64c^(15) -d^(27)$

we know that

$64=2^(6)=(2^(2))^(3)$ ------> the term is a perfect cube

$c^(15)=(c^(5))^(3)$ ------> the term is a perfect cube

$d^(27)=(d^(9))^(3)$ ------> the term is a perfect cube

Substitute

$64c^(15) -d^(27)=((2^(2))(c^(5)))^(3)-(d^(9))^(3)$

therefore

The expression $64c^(15) -d^(27)$ is a difference of cubes because all terms are perfect cubes

Answer 2

Answer:

The expression $\boxed{64{c^(15)} - {d^(27)}}$ is a difference of cubes.

Further Explanation:

Given:

The options are as follows,

(a). $9{w^(33)} - {y^(12)}$

(b). $18{p^(15)} - {q^(21)}$

(c). $36{a^(22)} - {b^(16)}$

(d). $64{c^(15)} - {a^(26)}$

(e). $64{c^(15)} - {d^(27)}$

Calculation:

The cubic formula can be expressed as follows,

$\boxed{{a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)}$

The expression is $9{w^(33)} - {y^(12)}.$

9 is not a perfect cube of any number, ${w^(33)}$ can be written as ${\left( {{w^(11)}} \right)^3}$ and ${y^(12)}$ can be represents as ${\left( {{y^4}} \right)^3}.$

$9{w^(33)} - {y^(12)}$ cannot be written as the difference of cube. Option (a) is not correct.

The expression is $18{p^(15)} - {q^(21)}.$

18 is not a perfect cube of any number, ${p^(15)}$ can be written as ${\left( {{p^5}} \right)^3}$ and ${q^(21)}$ can be written as ${\left( {{q^7}} \right)^3}.$

$18{p^(15)} - {q^(21)}$ cannot be written as the difference of cube. Option (b) is not correct.

The expression is $36{a^(22)} - {b^(16)}.$

36 is not a perfect cube of any number, ${a^(22)}$ is not perfect cube and ${b^(16)}$ is not a perfect cube.

$36{a^(22)} - {b^(16)}$ cannot be written as the difference of cube. Option (c) is not correct.

The expression is $64{c^(15)} - {a^(26)}.$

64 can be written as ${\left( {{2^2}} \right)^3}, {a^(26)}$ is not perfect cube and ${c^(15)}$ can be written as ${\left( {{c^5}} \right)^3}.$

$64{c^(15)} - {a^(26)}$ cannot be written as the difference of cube. Option (d) is not correct.

The expression is $64{c^(15)} - {d^(27)}.$

64 can be written as ${\left( {{2^2}} \right)^3}, {d^(27)}$ can be written as ${\left( {{d^9}} \right)^3}$ and ${c^(15)}$ can be written as ${\left( {{c^5}} \right)^3}.$

$\boxed{64{c^(15)} - {d^(27)} = {{\left( {{2^2}{c^5}} \right)}^3} - {{\left( {{d^9}} \right)}^3}}$

$64{c^(15)} - {d^(27)}$ can be written as the difference of cube. Option (e) is correct.

The expression $\boxed{64{c^(15)} - {d^(27)}}$ is a difference of cubes.

Learn more:

1. Learn more about unit conversion brainly.com/question/4837736

2. Learn more about non-collinear brainly.com/question/4165000

3. Learn more aboutbinomial and trinomial brainly.com/question/1394854

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Exponents and Powers

Keywords: Solution, factorized form, expression, difference of cubes, exponents, power, equation, power rule, exponent rule.

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