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Factoring out common factors

Factoring (high school)

Japanese school year: Junior high 3

What you learn

Take out the factor common to every term, sometimes followed by a formula.

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Key points

Use this when every term shares a common factor mm. Factoring out mm in front of parentheses is the fundamental first step in factoring.

ma+mb=m(a+b)ma + mb = m(a + b)

Use this when an expression has three or more terms sharing a common factor mm. Factoring out mm simplifies the entire expression.

ma+mb+mc=m(a+b+c)ma + mb + mc = m(a + b + c)

Use this when terms share a common grouped factor (a+b)(a + b). Treat (a+b)(a + b) as a single algebraic block and factor it out.

m(a+b)+n(a+b)=(m+n)(a+b)m(a + b) + n(a + b) = (m + n)(a + b)

After factoring out common factors, always check whether the expression inside the parentheses can be factored further.

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