Question

Which expression is equivalent to (3a + 7) (2a - 5)A. 5a^2 - a - 35B. 5a^2 -29a - 35C. 6a^2 - a - 35D. 6a^2 -29a - 35

Answer 1

We want to know an expression equivalent to:

`(3a+7)(2a-5)`

which is a multiplication. For doing it, we will use the distributive property, where we multiply the first term of the first expression by each one of the terms on the second expression, and then we multiply the second term of the first expression by each one of the terms on the second expression.

We obtain:

`=3a(2a)+3a(-5)+7(2a)+7(-5)`

Now, we multiply the terms as usual: first the coefficients and then the variables:

`\begin{gathered} =6a^2-15a+14a-35 \\ \text{And adding the similar terms we get:} \\ =6a^2-1a-35 \\ =6a^2-a-35 \end{gathered}`

Thus, the expression equivalent is 6a² - a - 35.