Solve 343b^2-7b^4

$$343 b ^ { 2 } - 7 b ^ { 4 }$$

Factor

$$7\left(-b-7\right)\left(b-7\right)b^{2}$$

Solution Steps

Factor out 7.

$$7\left(49b^{2}-b^{4}\right)$$

Consider 49b^{2}-b^{4}. Factor out b^{2}.

$$b^{2}\left(49-b^{2}\right)$$

Consider 49-b^{2}. Rewrite 49-b^{2} as 7^{2}-b^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(7-b\right)\left(7+b\right)$$

Reorder the terms.

$$\left(-b+7\right)\left(b+7\right)$$

Rewrite the complete factored expression.

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

Evaluate

$$343b^{2}-7b^{4}$$