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) * (2x + 9y)`