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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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