Solve ay^2-16a-5y^2+80

$$a y ^ { 2 } - 16 a - 5 y ^ { 2 } + 80$$

Factor

$$\left(a-5\right)\left(y-4\right)\left(y+4\right)$$

Solution Steps

Do the grouping ay^{2}-16a-5y^{2}+80=\left(ay^{2}-16a\right)+\left(-5y^{2}+80\right), and factor out a in the first and -5 in the second group.

$$a\left(y^{2}-16\right)-5\left(y^{2}-16\right)$$

Factor out common term y^{2}-16 by using distributive property.

$$\left(y^{2}-16\right)\left(a-5\right)$$

Consider y^{2}-16. Rewrite y^{2}-16 as y^{2}-4^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(y-4\right)\left(y+4\right)$$

Rewrite the complete factored expression.

$$\left(a-5\right)\left(y-4\right)\left(y+4\right)$$

Evaluate

$$\left(a-5\right)\left(y^{2}-16\right)$$