Question

clara found the product of $3 - 6y^2$ and $y^2 + 2$. her work is shown below.
$(3 - 6y^2)(y^2 + 2) = 3(y^2) + (-6y^2)(2)$
$= 3y^2 - 12y^2$
$= -9y^2$
is the student’s work correct?
$\bigcirc$ no, she did not multiply $-6y^2$ by 2 correctly
$\bigcirc$ no, she did not add $3y^2$ and $-12y^2$ correctly
$\bigcirc$ no, she did not use the distributive property correctly
$\bigcirc$ yes, she multiplied the binomials correctly

Explanation:

Step1: Recall distributive property

To multiply two binomials $(a+b)(c+d)$, use: $a(c+d)+b(c+d)=ac+ad+bc+bd$

Step2: Apply to given binomials

$$(3 - 6y^2)(y^2 + 2) = 3(y^2) + 3(2) + (-6y^2)(y^2) + (-6y^2)(2)$$

Step3: Calculate each term

$$= 3y^2 + 6 - 6y^4 - 12y^2$$

Step4: Compare to Clara's work

Clara only calculated $3(y^2) + (-6y^2)(2)$, missing $3(2)$ and $(-6y^2)(y^2)$. She failed to apply the full distributive property.

Answer:

No, she did not use the distributive property correctly