Sum and Difference of Cubes

Front

What is the formula for factoring the difference of cubes?

Back

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Tags

CCSS.HSA.APR.C.4

Front

What is the formula for factoring the sum of cubes?

Back

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Tags

CCSS.HSA.APR.C.4

Front

Factor the expression: 8x^3 - 1

Back

(2x - 1)(4x^2 + 2x + 1)

Tags

CCSS.HSA.APR.C.4

Front

Factor the expression: 27x^3 + 8

Back

(3x + 2)(9x^2 - 6x + 4)

Tags

CCSS.HSA.APR.C.4

Front

What is the result of factoring 64 - 27a^3?

Back

(4 - 3a)(9a^2 + 12a + 16)

Tags

CCSS.HSA.APR.C.4

Front

How do you factor the expression 2x^3 + 128?

Back

2(x + 4)(x^2 - 4x + 16)

Tags

CCSS.HSA.APR.C.4

Front

What is the factored form of x^3 + 1?

Back

(x + 1)(x^2 - x + 1)

Tags

CCSS.HSA.APR.C.4

Front

What is the significance of the coefficients in the sum and difference of cubes?

Back

The coefficients can affect the factors and the resulting quadratic expressions.

Tags

CCSS.HSA.APR.C.4

Front

How can you identify a sum or difference of cubes in an expression?

Back

Look for terms that are perfect cubes, such as a^3 and b^3.

Tags

CCSS.8.EE.A.2

Front

What is a perfect cube?

Back

A number that can be expressed as the cube of an integer, e.g., 1, 8, 27, 64.

Tags

CCSS.8.EE.A.2