Question

Which expression is equivalent to

(9x2 + 2x – 7)(x – 4)?
A. x(9x2 + 2x – 7) + 4(9x2 + 2x – 7)
B. (9x2 + 2x – 7)(x) + (9x2 + 2x – 7)(–4)
C. x(9x2 + 2x – 7) – 4
D. –4x(9x2 + 2x – 7)

Answer 1

I'm pretty sure its B. (9x2+2x-7)(x)+(9x2+2x-7)(-4)
Because its just splitting up the (x-4) and if you add the answers together then you get the same answer as the original

Answer 2

B.
`(9x^(2)+2x-7)(x)+(9x^(2)+2x-7)(-4)`

Explanation:

Given two expressions between parentheses that are multiplying between them, we can find the equivalent expression if we distribute the terms between them. For example :

The expression
`(a+b).(c+d)` is equivalent to

`(a+b).(c+d)=ac+ad+bc+bd` because we multiply the first element of the first expression (a+b) by the first element of the second expression (c+d) and then we sum the product between the first element of the expression (a+b) and the second element of the second expression (c+d).Then, we sum the product of the second element of the expression (a+b) and the first element of (c+d) and finally we sum the product of the second element of (a+b) and the second element of (c+d) in order to find the equivalent expression of (a+b).(c+d).

In the exercise :

`(9x^(2)+2x-7).(x-4)=(9x^(2))x+(9x^(2))(-4)+(2x)x+(2x)(-4)+(-7)x+(-7)(-4)`

Rearranging the expression we obtain :

`(9x^(2))x+(2x)x+(-7)x+(9x^(2))(-4)+(2x)(-4)+(-7)(-4)`

Factoring the expression :

`(9x^(2)+2x-7)(x)+(9x^(2)+2x-7)(-4)`

The correct answer is B.