 # Multiplying Algebraic Expressions

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In these lessons, we will learn how to multiply algebraic expressions.

How to Multiply a Term and an Algebraic Expression?

We will first consider examples of multiplying a term and an algebraic expression.

Example: Solution: How to Multiply Two Algebraic Expressions?

Next, we will also consider the multiplication of two algebraic expressions:
(a + b)(c + d)

Such an operation is called ‘expanding the expression ’.
To expand the expression, we multiply each term in the first pair of brackets by every term in the second pair of brackets.

Example:

Expand the following:

a) (y – 3)(2y + 5)
b) (a + b)2

Solution:

a) (y – 3)(2y + 5)
= y(2y+ 5) – 3(2y + 5)
= (y × 2y) + (y × 5) + (–3 × 2y) + (–3 × 5)
= 2y2 + 5y – 6y – 15
= 2y2 – y – 15

b) (a + b)2
= (a + b)(a + b) = a(a + b) + b(a + b)
= a2 + ab + ab + b2
= a2 + 2ab + b2

Here are some common expansions that you will find useful to remember: Multiplication of Algebraic Expressions:
1. Multiply the numbers (numerical coefficients)
2. Multiply the letters (literal numbers) - Exponents can only be combined if the base is the same.
Examples:
1. -2c2(-7c3x5)(bx2)2 =
2. 3a2(-ab4)(2a2c3) =
3. 3sy(s - t) =
4. 4uv2(3u2z - 7u3) Examples of multiplying expressions using the distributive property
Examples:
1. (x + 2)(x + 3)
2. (5x + 9)(4x - 2)
3. (2x + y)(3x + 2y)
4. (2x + 2)2 Multiplication of Algebraic Expressions - Use the distributive property
Examples:
1. 3cy2(-4cx - 2xy3)
2. (x + 5)(x -2) Multiplication of Algebraic Expressions - Solving Complex Questions
Examples:
1. (b + 3c)2
2. (2y - 4)3

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