Q. 383

In the following exercise, factor completely using the perfect square trinomials pattern.

$25 x^{2} + 30 x + 9$

Verified

Answer

The factorisation of the given polynomial

$25 x^{2} + 30 x + 9 = {(5 x + 3)}^{2}$

1Step 1. Given information

The given polynomial is:

$25 x^{2} + 30 x + 9$

2Step 2. Factorise the polynomial

We know that,

${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$

For polynomial $25 x^{2} + 30 x + 9$ , we have:

$25 x^{2} + 30 x + 9 {(5 x)}^{2} + 2 \times 5 x \times 3 + 3^{2} {(5 x + 3)}^{2} [u \sin g {(a + b)}^{2} = a^{2} + 2 a b + b^{2}]$

Thus, the factorisation of the given polynomial

$25 x^{2} + 30 x + 9 = {(5 x + 3)}^{2}$

3Step 3. check the answer

Multiplying the factors, we have:

$25 x^{2} + 30 x + 9 = {(5 x + 3)}^{2} 25 x^{2} + 30 x + 9 = (5 x + 3) (5 x + 3) 25 x^{2} + 30 x + 9 = 25 x^{2} + 30 x + 9$

This is true.