Question

Apply the distributive property. $$(7-2 a)(4 a)$$

Short answer

-8a^2 + 28a

Step-by-step solution

Distribute 4a to 7 and -2a

To simplify the expression, distribute (multiply) the term \(4a\) to both \(7\) and \(-2a\). This is done according to the distributive property \(a(b+c) = a*b+a*c\). In this case, \(a\) is \(4a\) and \(b\) and \(c\) are \(7\) and \(-2a\) respectively.

Multiply 4a to each term inside the parantheses

Multiply \(4a\) to \(7\), which equals to \(28a\). Then, multiply \(4a\) to \(-2a\) that gives \(-8a^2\).

Combine like terms

In this step, we have simplified the expression fully. As there are no like terms to combine, this is our final expression, which is \(-8a^2 + 28a\).