Solve 7r^4-112

$$7 r ^ { 4 } - 112$$

Factor

$$7\left(r-2\right)\left(r+2\right)\left(r^{2}+4\right)$$

Solution Steps

Factor out 7.

$$7\left(r^{4}-16\right)$$

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

$$\left(r^{2}-4\right)\left(r^{2}+4\right)$$

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

$$\left(r-2\right)\left(r+2\right)$$

Rewrite the complete factored expression. Polynomial r^{2}+4 is not factored since it does not have any rational roots.

$$7\left(r-2\right)\left(r+2\right)\left(r^{2}+4\right)$$

Evaluate

$$7\left(r^{4}-16\right)$$