Page 46 - 新思维数学学生用书8 样章

2.4 Factorising

2.4 Factorising

In this section you will … Key words

• use the HCF to factorise an expression. factorisations

factorise
To expand a term with brackets, you multiply 4(x + 3) = 4x + 12

each term inside the brackets by the term highest common
outside the brackets. factor (HCF)
When you factorise an expression, you take the
highest common factor (HCF) and put it outside 4x + 12 = 4(x + 3)
the brackets.

Worked example 2.4

Factorise these expressions.
2
a 2x + 10 b 8 − 12y c 4a + 8ab d x − 5 x
Answer
a 2x + 10 = 2(x + 5) The HCF of 2x and 10 is 2, so put 2 outside the brackets.
Divide both terms by 2 and put the results inside the brackets.
Check the answer by expanding: 2 × x = 2x and 2 × 5 = 10.

b 8 − 12y = 4(2 − 3y) The HCF of 8 and 12y is 4, so put 4 outside the brackets.
Divide both terms by 4 and put the results inside the brackets.
Check the answer by expanding: 4 × 2 = 8 and 4 × −3y = −12y.

c 4a + 8ab = 4a(1 + 2b) The HCF of 4a and 8ab is 4a, so put 4a outside the brackets.
Divide both terms by 4a and put the results inside the brackets.
Check the answer: 4a × 1 = 4a and 4a × 2b = 8ab.
d x −5x = x(x − 5) The HCF of x and 5x is x, so put x outside the brackets.
2
2
Divide both terms by x and put the results inside the brackets.
Check the answer: x × x = x and x × −5 = −5x.
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