Solve 6x^2y+28xy+30y

$$6 x ^ { 2 } y + 28 x y + 30 y$$

Factor

$$2y\left(x+3\right)\left(3x+5\right)$$

Solution Steps

Factor out 2.

$$2\left(3x^{2}y+14xy+15y\right)$$

Consider 3x^{2}y+14xy+15y. Factor out y.

$$y\left(3x^{2}+14x+15\right)$$

Consider 3x^{2}+14x+15. Factor the expression by grouping. First, the expression needs to be rewritten as 3x^{2}+ax+bx+15. To find a and b, set up a system to be solved.

$$a+b=14 ab=3\times 15=45$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 45.

$$1,45 3,15 5,9$$

Calculate the sum for each pair.

$$1+45=46 3+15=18 5+9=14$$

The solution is the pair that gives sum 14.

$$a=5 b=9$$

Rewrite 3x^{2}+14x+15 as \left(3x^{2}+5x\right)+\left(9x+15\right).

$$\left(3x^{2}+5x\right)+\left(9x+15\right)$$

Factor out x in the first and 3 in the second group.

$$x\left(3x+5\right)+3\left(3x+5\right)$$

Factor out common term 3x+5 by using distributive property.

$$\left(3x+5\right)\left(x+3\right)$$

Rewrite the complete factored expression.

$$2y\left(3x+5\right)\left(x+3\right)$$

Evaluate

$$2y\left(x+3\right)\left(3x+5\right)$$