Difference of two squares
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ATeaching
Example 1
Factorise x² − 49
- 1Notice that there are two square terms (a square letter and a square number) with a subtraction sign between them.
- 2This is the difference of two squares and is factorised into double brackets. Write the double brackets:
( )( ) - 3Work out the square root of x² and write this at the start of each bracket:
√x² = x
(x )(x ) - 4Work out the square root of 49 and write this at the end of each bracket:
√49 = 7
(x 7)(x 7) - 5Put a + between the terms in one bracket and a − in the other.
(x + 7)(x − 7)
Example 2
Factorise 4x² − 25
- 1Notice that there are two square terms (a squared term and a square number) with a subtraction sign between them.
- 2This is the difference of two squares and is factorised into double brackets. Write the double brackets:
( )( ) - 3Work out the square root of 4x² and write this at the start of each bracket:
√4x² = 2x
(2x )(2x ) - 4Work out the square root of 25 and write this at the end of each bracket:
√25 = 5
(2x 5)(2x 5) - 5Put a + between the terms in one bracket and a − in the other.
(2x + 5)(2x − 5)
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CWorksheet
Difference of two squares
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