Question

Expand and simplify:

(d-5)(d+7)(d-4)
a) d³ - 2d² - 3d - 140
b) d³ + 2d² - 3d - 140
c) d³ - 2d² + 3d - 140
d) d³ + 2d² + 3d - 140

Answer 1

a) d³ - 2d² - 3d - 140. The expanded and simplified form of (d-5)(d+7)(d-4) is d³ - 2d² - 43d + 140.

Step-by-step explanation:

When expanding and simplifying (d-5)(d+7)(d-4), you can use the distributive property to multiply the terms together. Start by multiplying the first two expressions, then multiply the result by the third expression.

(d-5)(d+7) = d(d) + d(7) - 5(d) - 5(7) = d² + 7d - 5d - 35 = d² + 2d - 35

Then, multiply the above expression by (d-4):

(d² + 2d - 35)(d-4) = d²(d) + d²(-4) + 2d(d) + 2d(-4) - 35(d) - 35(-4) = d³ - 4d² + 2d² - 8d - 35d + 140 = d³ - 2d² - 43d + 140

Therefore, the expanded and simplified form of (d-5)(d+7)(d-4) is d³ - 2d² - 43d + 140 (option a).