Question

Simplify the variable expression. $$4(3 x+5 y)+3(-4 x+2 y)$$

Short answer

The simplified expression is \(26y\).

Step-by-step solution

Apply the Distributive Property

We have an expression \(4(3 x+5 y)+3(-4 x+2 y)\). By applying the distributive property (i.e. multiplying the outside number with each term inside the parentheses), this expression becomes \(12x + 20y -12x + 6y\).

Combine Like Terms

Next, we combine the like terms in the equation. Like terms are terms whose variables (and their exponents such as the 2 in \(x^2\)) are the same. In this expression, the like terms are the terms with \(x\) and the terms with \(y\). We combine these to form \(0x + 26y\).

Simplify to Obtain Final Expression

A variable term multiplied by zero disappears from the equation, so our final expression is \(26y\).