Solve a^2-21a^2+20

$${ a }^{ 2 } -21 { a }^{ 2 } +20$$

Factor

$$20\left(-a-1\right)\left(a-1\right)$$

Solution Steps

Multiply and combine like terms.

$$-20a^{2}+20$$

Factor out 20.

$$20\left(-a^{2}+1\right)$$

Consider -a^{2}+1. Rewrite -a^{2}+1 as 1^{2}-a^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(1-a\right)\left(1+a\right)$$

Reorder the terms.

$$\left(-a+1\right)\left(a+1\right)$$

Rewrite the complete factored expression.

$$20\left(-a+1\right)\left(a+1\right)$$

Evaluate

$$20-20a^{2}$$

Solution Steps

Combine a^{2} and -21a^{2} to get -20a^{2}.

$$-20a^{2}+20$$