Distributive property?

Question

a. (x + 4)(x + 7)
b. (2t + 3)(3t - 5)
c. (4r - 3)(3r - 2)
d. (x squared + 3x + 2)(x + 6)

Answer 1

(x + 4) (x + 7)
= x(x + 7) + 4(x + 7)
= x^2 + 7x + 4x + 7
= x^2 + 11x + 7.

(2t + 3) (3t - 5)
= 2t (3t - 5) + 3(3t - 5)
= 2t(3t) + 2t(-5) + 3(3t) + 3(-5)
= 6t^2 - 10t + 9t - 15
= 6t^2 - t - 15.

You can also distribute the other bracket first:
(4r - 3)(3r - 2)
= (4r - 3)(3r) + (4r - 3)(-2)
= 12r^2 - 9r - 8r + 6
= 12r^2 - 17r + 6

(x^2 + 3x + 2) (x + 6)
= (x^2 + 3x + 2) x + (x^2 + 3x + 2) (6)
= x^3 + 3x^2 + 2x + 6x^2 + 18x + 12
= x^3 + 9x^2 + 20x + 12.

Answer 2

You actually use the FOIL method, which is close to the Distributive Property. It stands for First Outer Inner Last.
So for part a, you would do the First 2 terms (in each parenthesis), then the Outer 2 terms, the Inner 2 terms, and finally the Last 2 terms:
First terms: x times x = x^2
Outer terms: x times 7 = 7x
Inner terms: 4 times x = 4x
Last terms: 4 times 7 = 28

So we have x^2 +7x + 4x + 28 [then you combine the like terms] =
x^2 +11x +28

b. 6t^2 -10t +6t -15 = 6t^2 -4t -15

c. 12r^2 -8r -9r +6 = 12r^2 -17r +6

Hope this helps!

Answer 3

a. x^2 +11x+28
b. 6t^2 - t - 15
c. 12r^2 -17r +6
d. x^3 +6x^2 +3x^2 +18x +2x +12
=x^3 + 9x^2+20x+12

Answer 4

( Please Excuse My Dear Aunt Sally) PEMDAS

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