Question

$3xy - 24x^{4}y =$

Explanation:

Step1: Factor out GCF

Identify and factor out the greatest common factor $3xy$ from both terms.
$3xy - 24x^4y = 3xy(1 - 8x^3)$

Step2: Recognize difference of cubes

Rewrite the remaining expression as a difference of cubes, since $8x^3=(2x)^3$.
$1 - 8x^3 = 1^3 - (2x)^3$

Step3: Apply difference of cubes formula

Use the difference of cubes identity $a^3 - b^3=(a-b)(a^2+ab+b^2)$ where $a=1$, $b=2x$.
$1^3 - (2x)^3=(1-2x)(1+2x+4x^2)$

Step4: Combine all factors

Substitute the factored form back into the expression from Step1.
$3xy(1 - 8x^3)=3xy(1-2x)(1+2x+4x^2)$

Answer:

$3xy(1-2x)(1+2x+4x^2)$