Question

expand and state your answer as a polynomial in standard form.
$(4x - y^3)^2$

Explanation:

Step1: Apply square of difference formula

Recall the formula $(a-b)^2 = a^2 - 2ab + b^2$, where $a=4x$, $b=y^3$.

Step2: Calculate $a^2$

$a^2=(4x)^2=16x^2$

Step3: Calculate $-2ab$

$-2ab=-2(4x)(y^3)=-8xy^3$

Step4: Calculate $b^2$

$b^2=(y^3)^2=y^6$

Step5: Combine the terms

Add the results from Steps 2-4.
$16x^2 - 8xy^3 + y^6$

Answer:

$16x^2 - 8xy^3 + y^6$