Question

y2 + 2y - 48 factorize it​

Answer 1

⠀⠀⠀⠀Given :-

It is given to factorize the given expression :-

$\sf{ {y}^{2} + 2y - 48}$

⠀⠀⠀Factorisation :-

Here, we can factorize the expression as follows;

$\sf{ {y}^{2} + 2y - 48}$

• Factor the expression by grouping. First, the expression needs to be rewritten as $ \sf{ y^{2}+ay+by-48} $. To find a and b, set up a system to be solved.

$\to \sf{a+b=2 }\\ \to\sf{ab=1\left(-48\right)=-48 }$

$\sf-1,48 \\ \sf -2,24 \\ \sf-3,16 \\ \sf-4,12 \\ \sf -6,8$

• Now, calculate Sum for each;

$\sf{-1+48=47 }\\ \sf{ -2+24=22} \\ \sf{ -3+16=13 } \\ \sf{-4+12=8} \\ \sf{ -6+8=2 }$

• Thus, the solution is the pair that gives sum 2.

$\: \: \: \: \to \sf{a=-6 } \\ \to \sf{b=8 }$

Thus,

$\leadsto \sf{\left(y^{2}-6y\right)+\left(8y-48\right) }$

$\leadsto \sf{y\left(y-6\right)+8\left(y-6\right) }$

$\leadsto { \pmb{ \sf{ \color{red}{\left(y-6\right)\left(y+8\right) }}}}$

• ∴ Hence, the factorisation for the equation will be (y - 6)(y + 8).