Question

factorization of y^2 + y/6 - 1/6​

Answer 1

Answer:

Analysis→

Here we're given and equation $\rm{y^2+\dfrac{y}{6}-\dfrac{1}{6}}$ and we've to factorise the equation. And to ease the calculation, we can multiply the whole equation by a +integer to remove its fractional part. Hence we've to multiply the whole equation by 6.

Given→

• Equation = $\rm{y^2+\dfrac{y}{6}-\dfrac{1}{6}}$

To Perform→

Factorisation of the equation.

Answer→

$\rm\rightarrow{y^2+\dfrac{y}{6}-\dfrac{1}{6}}$

$\rm\rightarrow{6\times(y^2+\dfrac{y}{6}-\dfrac{1}{6})}$

$\rm\rightarrow{6y^2+y-1}$

$\rm\rightarrow{6y^2+3y-2y-1}$

$\rm\rightarrow{3y(2y+1)-1(2y+1)}$

$\rm\rightarrow{(3y-1)(2y+1)}$

$\rm\rightarrow{(\dfrac{1}{2}y-\dfrac{1}{6})(\dfrac{1}{3}y+\dfrac{1}{6})}$

☞ As we've multiplied the whole equation by 6 to ease the calculation. We've to divide it by 6 to get the final factors. Hence the factors are:-

$\rm{\dfrac{1}{2}y-\dfrac{1}{6}}$

and

$\rm{\dfrac{1}{3}y+\dfrac{1}{6}}$

HOPE IT HELPS.