Page 14 - Algebra 1

Factoring & Simplifying Algebraic Expressions
• When a given algebraic expression is a product of two or more expressions, each term of the expression is known as the factor of the algebraic expression.
For example,
3a, b, 3ab, ab,3 are the factors of expression 3ab
2 and(m2 + n2) are the factors of the expression 2(m2 + n2)
• Factorization is the process of writing an expression as a product of two or more expressions. For example,
2x3 +4x2 –8xcanbefactorizedas2x(x2 +2x–4)
• You can factorize a binominal by taking out the greatest common factor from the expression. In the above example, the GCF is 2x.
Factorization by splitting the middle term
Let’s understand it with an example, Ifyouwanttofindthefactorsofax2 +bx+c
This is not of the form of any identity you have previously studied. So, we will split the middle term as mx + nx.
The value of m and n should be such that m + n = b and mn = c
Worked Example 6
Factorize the following quadratic expression.
4x2 +8x+3
Solution:
=4x2 +8x+3
=4x2 +2x+6x+3
= 2x(2x + 1) + 3(2x + 1) = (2x + 3) + (2x + 1)
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ALGEBRA