Question

what is the product?
$(-2a^{2}+s)(5a^{2}-6s)$
$\bigcirc -10a^{4}+17a^{2}s-6s^{2}$
$\bigcirc -10a^{4}+17a^{4}s^{2}-6s^{2}$
$\bigcirc -10a^{4}-7a^{2}s-6s^{2}$
$\bigcirc -10a^{4}+17a^{2}s+6s^{2}$

Explanation:

Step1: Apply FOIL method (First terms)

Multiply first terms of each binomial:
$(-2a^2)(5a^2) = -10a^4$

Step2: Apply FOIL method (Outer terms)

Multiply outer terms of the binomials:
$(-2a^2)(-6s) = 12a^2s$

Step3: Apply FOIL method (Inner terms)

Multiply inner terms of the binomials:
$(s)(5a^2) = 5a^2s$

Step4: Apply FOIL method (Last terms)

Multiply last terms of each binomial:
$(s)(-6s) = -6s^2$

Step5: Combine all terms and simplify

Combine like terms ($12a^2s + 5a^2s$):
$-10a^4 + 12a^2s + 5a^2s - 6s^2 = -10a^4 + 17a^2s - 6s^2$

Answer:

$-10a^4 + 17a^2s - 6s^2$ (the first option)