5-7/5-5 Sum/Difference of Cubes & Perfect Square Binomials

Front

What is the formula for the difference of cubes?

Back

The difference of cubes can be factored using the formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Front

What is the formula for the sum of cubes?

Back

The sum of cubes can be factored using the formula: a^3 + b^3 = (a + b)(a^2 - ab + b^2).

Front

Factor the expression: 27x³ - 64

Back

(3x - 4)(9x² + 12x + 16)

Front

Factor the expression: x² - 25

Back

(x + 5)(x - 5) - This is a difference of squares.

Front

Factor the expression: x² - 100

Back

(x + 10)(x - 10) - This is a difference of squares.

Front

Factor the expression: 25x² - 36

Back

(5x + 6)(5x - 6) - This is a difference of squares.

Front

Factor the expression: 27x³ + 8

Back

(3x + 2)(9x² - 6x + 4) - This is a sum of cubes.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression of the form a² ± 2ab + b², which factors to (a ± b)².

Front

What is the difference between a sum of cubes and a difference of cubes?

Back

A sum of cubes involves adding two cubes (a³ + b³), while a difference of cubes involves subtracting two cubes (a³ - b³).

Front

What is the first step in factoring a polynomial?

Back

The first step is to look for a common factor in all terms of the polynomial.