Question

What is the factored form of the expression? 4x^2-81y^2

Answer 1

$4x^2-81y^2$ 

$(2x)^2-(9y)^2$ 

$(2x+9y)(2x-9y)$

Answer 2

$4x {}^{2} - 81y {}^{2}$
Write the expressions 4 & 81 in exponential form with an exponent of 2.

$= 2 {}^{2} x {}^{2} - 9 {}^{2} y {}^{2}$
Multiply the terms with equal exponents by multiplying their bases.

$= (2x) {}^{2} - (9y) {}^{2}$
Using
$a {}^{2} - b {}^{2} = (a - b)(a + b)$
Factor the expression.

$= (2x - 9y) \times (2x + 9y)$