Solve 4x^2y-12xy+5y

$$4 x ^ { 2 } y - 12 x y + 5 y$$

Factor

$$y\left(2x-5\right)\left(2x-1\right)$$

Solution Steps

Factor out y.

$$y\left(4x^{2}-12x+5\right)$$

Consider 4x^{2}-12x+5. Factor the expression by grouping. First, the expression needs to be rewritten as 4x^{2}+ax+bx+5. To find a and b, set up a system to be solved.

$$a+b=-12 ab=4\times 5=20$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 20.

$$-1,-20 -2,-10 -4,-5$$

Calculate the sum for each pair.

$$-1-20=-21 -2-10=-12 -4-5=-9$$

The solution is the pair that gives sum -12.

$$a=-10 b=-2$$

Rewrite 4x^{2}-12x+5 as \left(4x^{2}-10x\right)+\left(-2x+5\right).

$$\left(4x^{2}-10x\right)+\left(-2x+5\right)$$

Factor out 2x in the first and -1 in the second group.

$$2x\left(2x-5\right)-\left(2x-5\right)$$

Factor out common term 2x-5 by using distributive property.

$$\left(2x-5\right)\left(2x-1\right)$$

Rewrite the complete factored expression.

$$y\left(2x-5\right)\left(2x-1\right)$$

Evaluate

$$y\left(2x-5\right)\left(2x-1\right)$$