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What Are the Parentheses Rules?

On this page, we can see all the rules for parentheses in one spot.

Rule

Parentheses

(a + b) (c + d) = a c + a d + b c + b d a + (c + d) = a + c + d a (c + d) = a c d a (b + c) = a b + a c

(a + b) (c + d) = a c + a d + b c + b d a + (c + d) = a + c + d a (c + d) = a c d a (b + c) = a b + a c

Note! Remember to write the terms in descending order! Then it will look like this:

2x3 4x2 + 5x 3

2x3 4x2 + 5x 3

Example 1

Evaluate x + (2x + 5)

x + (2x + 5) = x 2x + 5 = x + 5

Example 2

Evaluate 4 (12 3x2)

4 (12 3x2) = 4 12 + 3x2 = 3x2 8

Example 3

Evaluate 4x2 (2 x)

4x2 (2 x) = 8x2 + 4x3 = 4x3 8x2

Example 4

Evaluate (x + 1) (x 2)

= (x + 1) (x 2) = x2 2x + x 2 = x2 x 2

(x + 1) (x 2) = x2 2x + x 2 = x2 x 2

Example 5

Evaluate (3x2 + y) (2 x)

= (3x2 + y) (2 x) = 6x2 3x3 + 2y xy = 3x3 + 6x2 xy + 2y

(3x2 + y) (2 x) = 6x2 3x3 + 2y xy = 3x3 + 6x2 xy + 2y

Example 6

Evaluate (2x + 3) (4x 5)

= (2x + 3) (4x 5) = 2x 4x + 2x (5) + 3 4x + 3 (5) = 8x2 + (10x) + 12x 15 = 8x2 + 2x 15

(2x + 3) (4x 5) = 2x 4x + 2x (5) + 3 4x + 3 (5) = 8x2 + (10x) + 12x 15 = 8x2 + 2x 15

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How Do You Multiply Parentheses?