Algebra: Squares, Cubes, and Factoring Formulas

$$1^2$$

$$1$$

$$2^2$$

$$4$$

$$3^2$$

$$9$$

$$4^2$$

$$16$$

$$5^2$$

$$25$$

$$6^2$$

$$36$$

$$7^2$$

$$49$$

$$8^2$$

$$64$$

$$9^2$$

$$81$$

$$10^2$$

$$100$$

$$2^3$$

$$8$$

$$3^3$$

$$27$$

$$4^3$$

$$64$$

$$5^3$$

$$125$$

$$6^3$$

$$216$$

$$7^3$$

$$343$$

$$8^3$$

$$512$$

$$9^3$$

$$729$$

$$10^3$$

$$1000$$

Difference of squares formula

$$a^2 - b^2 = (a + b)(a - b)$$

Sum of cubes formula

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

Difference of cubes formula

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

How to recognize a perfect square

A number with a whole-number square root (e.g., $49 = 7^2$)

How to recognize a perfect cube

A number with a whole-number cube root (e.g., $125 = 5^3$)

Factor $x^2 - 64$

$$(x + 8)(x - 8)$$

Factor $x^3 + 27$

$$(x + 3)(x^2 - 3x + 9)$$

Factor $x^3 - 125$

$$(x - 5)(x^2 + 5x + 25)$$