Question

Factorize the following expressions
20x²-45​

Answer 1

Answer:

here is your answer.

Step-by-step explanation:

5(4x²-9)

5[(2x)²-(3)²]

5(2x-3)(2x+3)

Answer 2

$\mathfrak{\large{\underline{\underline{Answer}}}}$

$\implies 20x^{2} -45$

$\implies 4\times 5 \times x\ -\ 9\times5$

$\implies 2^{2}\times5\times x \ -\ 3^{2}\times x$

Factor the GCF (Greatest Common Factor).↓↓

$\implies5 \bigg(\dfrac{2^{2}\times 5x^{2} }{5} \bigg)-\bigg(\dfrac{3x^{2}\times 5 }{5}\bigg)$

Reduce this fraction to the lowest terms.↓↓

$\implies 5\bigg(2^{2} \times x^{2} -(3^{2}) \bigg)$

$\implies 5(4^{2} -9)$

$\implies 5\bigg(2^{2} \times x\ -3 ^{2} \bigg)$

$\implies 5\bigg((2x^{2} )\ -3\bigg)$

Before factoring this expression as a difference of two squares, we need to make squares explicit.↓↓

The following rule will be applied:

A2N−B2=(AN)2−B2.

In our question,

•    A is equal to 2x.

•    B is equal to 3.

•    N is equal to 1.

$\implies 5\bigg(( 2x-3 )(2x+2)\bigg)$

$\implies5 (2x-3)(2x+3)$