Question

(viii) (3x + 1)^2 - (3x + 2) (3x - 1)​

Answer 1

Question:

$(3 {x} + 1) {}^{2} - (3x + 2)(3x - 1)$

Solution:

We will expand (3x+1)² using the following algebraic identity.

$\boxed{(a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab}$

We have

$\rightarrow \: (3x + 1) {}^{2} - (3x + 2)(3x - 1)$

$\small \: \implies \: (3x) {}^{2} + (1) {}^{2} + 2(3x)(1) - (3x + 2)(3x - 1) \\ \\ \small \implies\: 9{x}^{2} + 1 + 6x - (3x + 2)(3x - 1) \\ \\ \small \implies \: 9{x}^{2} + 1 + 6x - [ \: (3x)(3x - 1) + 2(3x - 1) \: ] \\ \\ \small \implies9{x}^{2} + 1 + 6x - [ \: 9 {x}^{2} \: - 3x + 6x - 2 \: ] \\ \\ \small \implies \: 9 {x}^{2} + 1 + 6x - [9 {x}^{2} + 3x - 2 ] \\ \\ \small \implies \: 9 {x}^{2} + 1 + 6x - 9 {x}^{2} - 3x + 2 \\ \\ \small \implies \: \cancel {9 {x}^{2} } - \cancel{9 {x}^{2} } + 6x - 3x + 2 + 1 \\ \\ \small \implies \: 3x + 3 \\ \\ \small \implies \:3(x + 1)$

Hope it helps you.