Question

Which expression is equivalent to (3x+2)(3x-5)?

A. 6x - 3
B. 9x^2 - 10
C. 9x^2 - 3x - 10
D. 9x^2 - 9 - 10

Answer 1

Answer: 9x^2 - 9x - 10 (choice D)

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Step-by-step explanation:

Let's make

y = 3x+2

So we can replace the (3x+2) with y

We go from (3x+2)(3x-5) to y(3x-5)

Distribute that y term through

y(3x-5)

y(3x) + y(-5)

3xy - 5y

Then plug in y = 3x+2 and distribute two more times

3xy - 5y

3x( y ) - 5( y )

3x( 3x+2 ) - 5( 3x+2 )

3x(3x) + 3x(2) - 5(3x) - 5(2)

9x^2 + 6x - 15x - 10

9x^2 - 9x - 10

which seems to point to choice D assuming the -9 in the middle is supposed to be -9x

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Side note: Alternative methods are the FOIL rule and the box method.

Answer 2

Answer: 9x^2-9x-10 ==> D

Step-by-step explanation:

(3x+2)(3x-5)=

3x*3x + (-5)(3x) + 2*3x + (-5)(2)=

9x^2 - 5(3x) + 6x - 5(2)=

9x^2-15x+6x-10=

9x^2-15x+6x-10= 9x^2-9x-10 ==> D