Question

multiply.
(2ab + 5c)(2ab − 5c)
(2ab + 5c)(2ab − 5c) = \square (simplify your answer.)

Explanation:

Step1: Apply difference of squares rule

Recall that $(x+y)(x-y)=x^2-y^2$. Here $x=2ab$, $y=5c$.

Step2: Calculate $x^2$

$(2ab)^2 = 2^2 \cdot a^2 \cdot b^2 = 4a^2b^2$

Step3: Calculate $y^2$

$(5c)^2 = 5^2 \cdot c^2 = 25c^2$

Step4: Substitute into the formula

$x^2 - y^2 = 4a^2b^2 - 25c^2$

Answer:

$4a^2b^2 - 25c^2$