Question

Complete the factorization of 4x2 – 9.



4x2 – 9 = ( x – )( x + )

Answer 1

`\huge{ANSWER}`

`{2x}^(2) - {3}^(2)`

so by identity

`{a}^(2) - {b}^(2) = (a + b)(a - b)`

(2x+3)(2x-3)✔✔✔

Answer 2

`\large\boxed{4x^2-9=(2x-3)(2x+3)}`

Explanation:

`4x^2-9\\\\METHOD\ 1:\\\\4x^2+6x-6x-9=2x(2x+3)-3(2x+3)=(2x-3)(2x+3)\\\\METHOD\ 2:\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\4x^2=2^2x^2=(2x)^2\\9=3^2\\\\4x^2-9=(2x)^2-3^2=(2x-3)(2x+3)`