Solve 7st^4-7sm^4

$$7 s t ^ { 4 } - 7 s m ^ { 4 }$$

Factor

$$7s\left(t-m\right)\left(m+t\right)\left(m^{2}+t^{2}\right)$$

Solution Steps

Factor out 7.

$$7\left(st^{4}-sm^{4}\right)$$

Consider st^{4}-sm^{4}. Factor out s.

$$s\left(t^{4}-m^{4}\right)$$

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

$$\left(t^{2}-m^{2}\right)\left(t^{2}+m^{2}\right)$$

Reorder the terms.

$$\left(-m^{2}+t^{2}\right)\left(m^{2}+t^{2}\right)$$

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

$$\left(t-m\right)\left(t+m\right)$$

Reorder the terms.

$$\left(-m+t\right)\left(m+t\right)$$

Rewrite the complete factored expression.

$$7s\left(-m+t\right)\left(m+t\right)\left(m^{2}+t^{2}\right)$$

Evaluate

$$7s\left(t^{4}-m^{4}\right)$$