Question

simplify each product (3p²+10q)(3p²-10q) 9p²+1q 6p⁴+20q 9p⁴-100q² 9p²+100q

Explanation:

Step1: Recognize difference of squares

The expression $(3p^2+10q)(3p^2-10q)$ fits the difference of squares pattern $(a+b)(a-b)=a^2-b^2$, where $a=3p^2$ and $b=10q$.

Step2: Calculate $a^2$

$a^2=(3p^2)^2=9p^4$

Step3: Calculate $b^2$

$b^2=(10q)^2=100q^2$

Step4: Substitute into difference formula

$a^2 - b^2 = 9p^4 - 100q^2$

Answer:

$9p^4-100q^2$