Algebraic Expansion

Algebraic expansion is a term with variables inside and outside of the brackets

. Multiplying each term on outside the bracket can be multiplied by each and every term inside the bracket. Expansion of the expression is called as algebraic expansion. The variables x, y, z and constant terms are included in the expression. For example, the expression is x (2x + 4). Let us see about algebraic expansion in this article.

Worked Examples to Algebraic Expansion

Example 1:

Solve the algebraic expansion 3(2 + 6x)

Solution:

Step 1:

Let us write the given expression as 3(2 + 6x).

Step 2:

Multiply each term inside the bracket with the term outside of the bracket.

3 2 = 6

3 6x = 18x

Therefore, the solution for multiplying the expression is 18x.

Example 2:

Solve the algebraic expansion 4x(2 + 7x) y(2 + 3x)

Solution:

Step 1:

Solve the first term,

4x(2 + 7x)

4x 2 = 8x

4x 7x = 28x2

Step 2:

Combining the terms in step (1),

28x2 + 8x

Step 3:

Solve the second term,

-y 2 = - 2y

-y 3x = - 3xy

Step 4:

Combining the terms in step (3),

-2y 3xy

Step 5:

Combining the step (1) and step (2), we get,

28x2 + 8x -2y 3xy

Therefore, the solution for the given expression is 28x2 + 8x -2y 3xy.

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Example 3:

Solve the algebraic expression (2x + 3) (x + 5).

Solution:

Step 1:

Let us write the given expression as (2x + 3) (x + 5).

Step 2:

Multiply each term in first bracket is multiplied with every term in the second bracket, we get,

2x x = 2x2

2x 5 = 10x

3 x = 3x

3 5 = 15

Combine the terms, we get,

2x2 + 10x + 3x + 15

Adding the common x terms, we get,

2x2 + 13x + 15

Therefore, the solution for the given expression is 2x2 + 13x + 15.

Practice Problems to Algebraic Expansion

1. Solve the algebraic expansion 5x (2 + 3y).

Key: 10x + 15xy

2. Solve the algebraic expansion 3x (2x + 3y + 4z + 8).

Key: 9xy + 12xz + 30x

3. Solve the algebraic expansion 3(2 + 4z).

Key: 12z + 6

4. Solve the algebraic expansion 4(2x + 3y).

Key: 8x + 12y

by: mathqa

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