The distributive property states that a × (b + c) = ___ + ___.

(a × b) + (a × c)

If a and b are increased by 1, the product ab increases by ___.

a + b + 1

True or False: The identity a² – b² can be factored as (a + b)(a – b).

True

Expand the expression (x + 3)(x + 2) using the distributive property.

(x + 3)(x + 2)

= x(x + 2) + 3(x + 2)   

= (x² + 2x) + (3x + 6)

= x² + 2x + 3x + 6

= x² + 5x + 6

Using the identity for the square of a sum, (a + b)² = ___.

a² + 2ab + b²

Fill in the blank: The equation 2(a² + b²) = ___ + ___ describes a mathematical identity.

(a + b)² + (a – b)²

Calculate the result of 6 × (4 + 5) using the distributive property.

6 × (4 + 5)

= (6 × 4) + (6 × 5)

= 24 + 30

= 54

What happens to the product when both factors a and b are decreased by 1?

If both a and b are decreased by 1, the new product is:
(a − 1)(b − 1)

Using the distributive property:
(a − 1)(b − 1) = ab − a − b + 1

If you multiply 8 by (3 + 2), the result is equal to ___ using the distributive property.

8 × 3 + 8 × 2 = 40

Using the identity for the square of a difference, (a - b)² = ___.

a² - 2ab + b²

What is the product of (x + 1)(x + 4) when expanded?

(x + 1)(x + 4)

= x(x + 4) + 1(x + 4)

= (x² + 4x) + (x + 4)

= x² + 4x + x + 4

= x² + 5x + 4

Fill in the blank: The distributive property can also be expressed as a(b + c) = ___ + ___.

ab + ac

Calculate the product of (10 - 3)(10 + 3) using the difference of squares.

difference of squares

(a − b)(a + b) = a² − b²

Here, a = 10 and b = 3.

(10 − 3)(10 + 3) = 10² − 3²
= 100 − 9
= 91

True or False: The product of two negatives results in a positive.

True