subject: Algebraic Expansion [print this page] 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.
