Difference of Squares / Cubes

What is the general form of a cubic polynomial?

• ax³ + bx² + cx + d, where a, b, c, and d are constants.

• ax² + bx + c, where a, b, and c are constants.

• a + b + c + d, where a, b, c, and d are constants.

• ax⁴ + bx³ + cx² + d, where a, b, c, and d are constants.

Factor the expression: 64x³ + 1

• (4x + 1)(16x² - 4x + 1)

• (8x + 1)(8x² - 8x + 1)

• (2x + 1)(32x² - 16x + 1)

• (4x - 1)(16x² + 4x + 1)

What is the sum of squares?

• The sum of squares cannot be factored over the real numbers.

• The sum of squares is always positive.

• The sum of squares can be factored into linear terms.

• The sum of squares is equal to the product of its roots.

Factor the expression: 121x² - 49

• (11x + 7)(11x - 7)

• (11x + 7)(11x + 7)

• (121x + 49)(x - 1)

• (11x - 7)(11x - 7)

Factor the expression: x³ - 343

• (x - 7)(x² + 7x + 49)

• (x - 7)(x² - 7x + 49)

• (x + 7)(x² - 7x + 49)

• (x - 7)(x² + 7x - 49)

What is the first step in factoring a difference of squares?

• Identify the squares and apply the difference of squares formula.

• Multiply the terms together to find the product.

• Add the squares to form a perfect square trinomial.

• Rewrite the expression as a sum of squares.

Factor the expression: 4y² - 9

• (2y + 3)(2y - 3)

• (2y + 3)(2y + 3)

• (4y - 3)(y + 3)

• (2y - 3)(2y - 3)

How do you recognize a difference of cubes?

• Look for a binomial where both terms are perfect cubes.

• Identify a trinomial with a leading coefficient of one.

• Check if the expression can be factored into two linear terms.

• Find a common factor in all terms of the expression.

What is a perfect square?

• A number that can be expressed as the square of an integer.

• A number that is the product of two different integers.

• A number that is always even.

• A number that has no integer square root.

What is the result of (a + b)(a - b)?

• a² + b² (sum of squares)

• a² - b² (difference of squares)

• a² - 2ab (expanded form)

• ab (product of a and b)