Question

Factorize: $1-2a-2b-3(a+b{)}^2$

• A. $(a+b-1)(1-3a+3b))$
• B. $(a+1)(1-3a-3b))$
• C. $(a+b+1)(1-3a-3b))$
• D. $(a+b+1)(1-3a-3))$

Answer 1

The correct option is C $(a+b+1)(1-3a-3b))$

$\Rightarrow 1-2a-2b-3(a+b{)}^2$

$\Rightarrow 1-2(a+b)-3(a+b{)}^2$

$\Rightarrow -3(a+b{)}^2-2(a+b)+1$

$\text{Let}(a+b)=x,$

$\Rightarrow -3x^2-2x+1$

$\Rightarrow -[3x^2+2x-1]$

$\Rightarrow -[3x^2+3x-1x-1]$

$\Rightarrow -\left[3x\right(x+1)-1(x+1\left)\right]$

$\Rightarrow -\left[\right(x+1\left)\right(3x-1\left)\right]$

$\Rightarrow (x+1)(1-3x)$

$\text{Substituting the value of x = (a+b), we get}$

$\Rightarrow (a+b+1)(1-3(a+b\left)\right)$

$\Rightarrow (a+b+1)(1-3a-3b))$