Solve 40k^2-90m^2=

$$40 k ^ { 2 } - 90 m ^ { 2 } =$$

Factor

$$10\left(2k-3m\right)\left(3m+2k\right)$$

Solution Steps

Factor out 10.

$$10\left(4k^{2}-9m^{2}\right)$$

Consider 4k^{2}-9m^{2}. Rewrite 4k^{2}-9m^{2} as \left(2k\right)^{2}-\left(3m\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2k-3m\right)\left(2k+3m\right)$$

Reorder the terms.

$$\left(-3m+2k\right)\left(3m+2k\right)$$

Rewrite the complete factored expression.

$$10\left(-3m+2k\right)\left(3m+2k\right)$$

Evaluate

$$40k^{2}-90m^{2}$$