Answer:
D) 4x - 17
E) -b - 6a
F) -2(7x + 34)
Step-by-step explanation:
For question D, we divide each term in the first binomial by 3x and simplify:
(12x² / 3x) - (51xy / 3x)
12 / 3 = 4, x² / x = x 51 / 3 = 17, x / x = 1, y / 1 = y
4x - 17(1)y
4x - 17y is left as a quotient
For question E, we do distribute -3a to the binomial in the numerator and do the same, divide each term in the binomial by -6a and simplify:
-3a(-2b - 12a) = -3a(-2b) - 3a(-12a) = 6ab + 36a²
(6ab + 36a²) / -6a =
(6ab / -6a) + (36a² / -6a)
6 / -6 = -1, a / a = 1, b / 1 = b 36 / -6 = -6, a² / a = a
-1(1)(b) + (-6)(a)
-b - 6a is left as a quotient
For question F, we distribute the 4 and 3x to their respective binomials and then combine like terms where applicable:
4(x² - 8x) + 3x(-6x - 12)
4(x²) + 4(-8x) + 3x(-6x) + 3x(-12)
4x² - 32x - 18x² - 36x
4x² - 18x² - 32x - 36x
-14x² - 68x, both terms have a greatest common factor (GCF) of -2 which can be divide out of them to further simplify:
-2(7x + 34)