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A3 Factorizing and substitution

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We can write the 5 outside of a set of brackets and mentally divide 5x + 10 by 5.

Factorizing expressions

Some expressions can be simplified by dividing each term by a common factor and writing the expression using brackets.

In the expression:

5x + 10

the terms 5x and 10 have a common factor, 5.

We can write the 5 outside of a set of brackets

5(x + 2)

(5x + 10) ÷ 5 = x + 2

This is written inside the bracket.

5(x + 2)

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Factorizing expressions

Writing 5x + 10 as 5(x + 2) is called factorizing the expression.

Factorize 6a + 8

6a + 8 = 2(3a + 4)

Factorize 12 – 9n

12 – 9n = 3(4 – 3n)

The highest common factor of 6a and 8 is 2.

(6a + 8) ÷ 2 = 3a + 4

The highest common factor of 12 and 9n is 3.

(12 – 9n) ÷ 3 = 4 – 3n

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Pelmanism: Equivalent expressions

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Substitution

What does substitution

mean?

In algebra, when we replace letters in an expression or equation with numbers we call it substitution.

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How can be written as an algebraic expression?4 + 3 ×

Using n for the variable we can write this as 4 + 3n.

We can evaluate the expression 4 + 3n by substituting different values for n.

When n = 5 4 + 3n = 4 + 3 × 5= 4 + 15= 19

When n = 11 4 + 3n = 4 + 3 × 11= 4 + 33= 37

Substitution

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Noughts and crosses – substitution

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