Solve y^2+8y)(c+d)+15(d+c)

$$y ^ { 2 } + 8 y ) ( c + d ) + 15 ( d + c )$$

Factor

$$y\left(y+8\right)$$

Solution Steps

Factor out y.

$$y\left(y+8\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$y^{2}+8y=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$y=\frac{-8±\sqrt{8^{2}}}{2}$$

Take the square root of 8^{2}.

$$y=\frac{-8±8}{2}$$

Now solve the equation y=\frac{-8±8}{2} when ± is plus. Add -8 to 8.

$$y=\frac{0}{2}$$

Divide 0 by 2.

$$y=0$$

Now solve the equation y=\frac{-8±8}{2} when ± is minus. Subtract 8 from -8.

$$y=-\frac{16}{2}$$

Divide -16 by 2.

$$y=-8$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and -8 for x_{2}.

$$y^{2}+8y=y\left(y-\left(-8\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$y^{2}+8y=y\left(y+8\right)$$

Evaluate

$$y\left(y+8\right)$$