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

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**How to Multiply a Term and an Algebraic Expression?**

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

**How to Multiply Two Algebraic Expressions?**

Next, we will also consider the multiplication of two algebraic expressions:*y* – 3)(2*y* + 5)

b) (*a* + *b*)^{2}

*y* – 3)(2*y* + 5)

=*y*(2*y*+ 5) – 3(2*y* + 5)

= (*y* × 2*y*) + (*y* × 5) + (–3 × 2*y*) + (–3 × 5)

= 2*y*^{2} + 5*y *– 6*y* – 15

= 2*y*^{2} – *y* – 15

b) (*a* + *b*)^{2}

= (*a* + *b*)(*a* + *b*) = *a*(*a* + *b*) + *b*(*a* + *b*)

=*a*^{2} + *ab* + *ab* + *b*^{2}

=*a*^{2} + 2*ab* + *b*^{2}

**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. -2c^{2}(-7c^{3}x^{5})(bx^{2})^{2} =

2. 3a^{2}(-ab^{4})(2a^{2}c^{3}) =

3. 3sy(s - t) =

4. 4uv^{2}(3u^{2}z - 7u^{3})
**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. 3cy^{2}(-4cx - 2xy^{3})

2. (x + 5)(x -2)**Multiplication of Algebraic Expressions - Solving Complex Questions**

Examples:

1. (b + 3c)^{2}

2. (2y - 4)^{3}

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Related Topics:

More Lessons on Algebra

Algebra Worksheets

Algebra Games

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

* Example: *

Evaluate:

a) 2*p*(3*pq* – 5*qr*)

b)

* Solution: *

a) 2*p*(3*pq* – 5*qr*)

= [2*p**× *3*pq*] + [2*p**× *(–5*qr*)]

= 6*p*^{2}*q* – 10*pqr *

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) (b) (

* Solution: *

=

= (

= 2

= 2

b) (

= (

=

=

Here are some common expansions that you will find useful to remember:

(

a+b)^{2}=a^{2}+ 2ab+b^{2}(

a–b)^{2}=a^{2}– 2ab+b^{2}(

a+b)(a–b) =a^{2}–b^{2}

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. -2c

2. 3a

3. 3sy(s - t) =

4. 4uv

Examples:

1. (x + 2)(x + 3)

2. (5x + 9)(4x - 2)

3. (2x + y)(3x + 2y)

4. (2x + 2)

Examples:

1. 3cy

2. (x + 5)(x -2)

Examples:

1. (b + 3c)

2. (2y - 4)

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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