Solve mathfrakg^2-4mathfrakb^2

$$\mathfrak { g } ^ { 2 } - 4 \mathfrak { b } ^ { 2 }$$

Factor

$$\left(g-2b\right)\left(2b+g\right)$$

Solution Steps

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

$$\left(g-2b\right)\left(g+2b\right)$$

Reorder the terms.

$$\left(-2b+g\right)\left(2b+g\right)$$

Evaluate

$$g^{2}-4b^{2}$$