Sum of cubes:

(a + b)(a2 – ab + b2) = a3 + b3

Difference of cubes:

(a – b)(a2 + ab + b2) = a3 – b3

Which products result in a sum or difference of cubes? Check all that apply.

(x - 1)(x² + x + 1) = x³ - 1³  and (x + 4)(x² - 4x + 16) = x³ + 4³

Step-by-step explanation:

complete question is: Check all that apply.

(x – 4)(x2 + 4x – 16)

(x – 1)(x2 – x + 1)

(x – 1)(x2 + x + 1)

(x + 1)( + x – 1)

(x + 4)(x2 – 4x + 16)

(x + 4)(x2 + 4x + 16)

SOLUTION:

Formulas for sum of cubes and difference of cubes are:

x³ +y³ = (x + y) (x²- xy + y²)

x³ - y³=(x - y)(x² + xy + y²)

So,

->(x - 1)(x² + x + 1) = x³ - 1³

The above statement yields the difference of cubes.

->(x + 4)(x² - 4x + 16) = x³ + 4³

The above statement yields the sum of cubes.

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)

the solution, from the graphing of the two lines, is (3,2), i.e., x = 3, y = 2.