Solve 28a^2+14a^2-21a^4

$$28 a ^ { 2 } + 14 a ^ { 2 } - 21 a ^ { 4 }$$

Factor

$$21a^{2}\left(2-a^{2}\right)$$

Solution Steps

Factor out 7.

$$7\left(4a^{2}+2a^{2}-3a^{4}\right)$$

Consider 4a^{2}+2a^{2}-3a^{4}. Factor out a^{2}.

$$a^{2}\left(6-3a^{2}\right)$$

Consider 4+2-3a^{2}. Multiply and combine like terms.

$$-3a^{2}+6$$

Consider -3a^{2}+6. Factor out 3.

$$3\left(-a^{2}+2\right)$$

Rewrite the complete factored expression.

$$21a^{2}\left(-a^{2}+2\right)$$

Simplify. Polynomial -a^{2}+2 is not factored since it does not have any rational roots.

$$21\left(-a^{2}+2\right)a^{2}$$

Evaluate

$$42a^{2}-21a^{4}$$

Solution Steps

Combine 28a^{2} and 14a^{2} to get 42a^{2}.

$$42a^{2}-21a^{4}$$