Question

Use the distributive property and mental math to simplify the expression. $$ -6 w-12-3 w+2 x^{2} $$

Short answer

The simplified version of the expression \(-6w -12 -3w + 2x^2\) is \(2x^2 -9w -12\).

Step-by-step solution

Group-like Terms Together

In the expression \(-6w -12 -3w + 2x^2\), we can first group together the similar types of terms together: \(-6w -3w + -12 + 2x^2\). Here we moved the terms that had 'w' together, and clubbed the constant (-12) and the term with 'x' together.

Apply Distributive Property

After grouping, apply the distributive property to simplify the 'w' terms: \((-6 -3)w + (-12) + 2x^2\), which simplifies further to \(-9w - 12 + 2x^2\). The distributive property allows us to combine like terms by adding or subtracting their coefficients.

Rearrange for Better Reading

Lastly, to better structure the simplified expression, you might want to place the term with the highest exponent first: \(2x^2 -9w -12\). Higher degree terms are usually placed first for better readability.