Answer:
(4x+3)^2
Step-by-step explanation:
To figure out if you chose the correct answer, work backwards. Take (16x + 3)(x+3) and distribute everything in.
Make arrows from the 16x to both parts in the second half. Then make arrows from the 3 to both parts of the second parenthesis. You now have to multiply these arrows. (This part is for visual learners.)
So, 16x * x + 16x * 3 + 3 * x + 3 * 3 =
16x(^2) + 48x + 3x + 9
This answer would give you 16x (^2) +51x + 9.
So, that answer is not correct.
Let's test the other two, as well.
(4x + 3)(4x - 3)
4x * 4x + 4x * -3 + 3 * 4x + 3 * -3 =
16x(^2) + -12x + 12x + -9 =
Combine like terms:
16x(^2) + -12x + 12x + -9 =
the -12x + 12x give you 0. That leaves you with 16x(^2) -9. So, that's not the answer.
Let's test the last one.
(4x+3)^2
If you write this out, you will have (4x+3)(4x+3).
Let's solve this.
4x * 4x + 4x * 3 + 3 * 4x + 3 * 3 =
16x(^2) + 12x + 12x + 9 =
Combine like terms:
16x(^2) + 12x + 12x + 9 =
16x(^2) + 24x + 9
That is the answer we need!
