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Home > Maths I > Relationships > Simplifying algebraic terms and simple factorisation

Maths I

Simplifying algebraic terms and simple factorisation

Simplifying algebraic expressions

A student making silly faces behind his maths teacher's back.

Now we'll combine multiplying out brackets and collecting like terms, to simplify algebraic expressions.

Look at the expression 5(a + b) - 2b.

We want to simplify it:

5(a + b) - 2b

= 5a + 5b - 2b, when the brackets are multiplied out,

= 5a + 3b, when like terms are collected and combined.

Therefore,

5(a + b ) - 2b = 5a + 3b.

Example

Simplify 3(x - 2y) + 4x.

3(x - 2y) + 4x = 3x - 6y + 4x, on multiplying out the brackets,

= 7x - 6y, on collecting like terms.

Now, try these questions.

Question

Simplify 2(x + 7) + 3x + 2.

Answer

2x + 14 + 3x + 2 = 5x + 16

Question

Simplify 4(2a + 3b) - 6a - b.

Answer

8a + 12b - 6a - b = 2a + 11b

Question

Simplify 2(m + 5) - 4 + m.

Answer

2m + 10 - 4 + m = 3m + 6

Question

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

Answer

3x + 3y + 6x - 2y = 9x + y

Well done, if you got these all correct!

If you didn't, check through the answers carefully.

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