04 January 2022 Factorising the difference of two
- Slides: 8
04 January 2022 Factorising the difference of two squares LO: Factorise differences of squares. www. mathssupport. org
Factorizing the difference between two squares A quadratic expression in the form x 2 – a 2 is called the difference between two squares. The difference between two squares can be factorized as follows: x 2 – a 2 = (x + a)(x – a) For example, x 2 – 25 = (x + 5) (x – 5) 9 x 2 – 16 = (3 x + 4)(3 x – 4) 25 a 2 – 1 = (5 a + 1)(5 a – 1) m 4 – 49 n 2 = (m 2 + 7 n)(m 2 – 7 n) www. mathssupport. org
Factorizing the difference between two squares Fully factorise 2 a 2 – 8 Removing the common factor 2 2 a 2 – 8 = 2 ( a 2 – 4 ) We can see that the expression into brackets is the difference of two squares. Factorising the difference of two squares, 2 a 2 – 8 = 2 (a + 2)(a – 2) www. mathssupport. org
Factorizing the difference between two squares Fully factorise – 3 a 2 + 48 Removing the common factor – 3 a 2 + 48 = – 3 ( a 2 – 16 ) We can see now that the expression into brackets is the difference of two squares. Factorising the difference of two squares, – 3 a 2 + 48 = – 3 (a + 4)(a – 4) www. mathssupport. org
Factorizing the difference between two squares Fully factorise 2 x 2 – 8 Removing the common factor 2 2 x 2 – 8 = 2 ( x 2 – 4 ) We can see now that the expression into brackets is the difference of two squares. Factorising the difference of two squares, 2 x 2 – 8 = 2 (x + 2)(x – 2) www. mathssupport. org
Factorizing the difference between two squares Fully factorise x 2 – 7 7 is not a square number But we can write 7 as The expression can be written as x 2 – Factorising the difference of two squares, x 2 – = (x + ) (x – ) x 2 – 7 = www. mathssupport. org
Factorizing the difference between two squares Fully factorise (5 x + 3)2 – 16 Notice that the expression to the left is a square expression (5 x + 3)2 And the number to the right is a square number. 16 And it is a difference. Factorising the difference of two squares, (5 x + 3)2 – 16 = [ ( 5 x + 3) + 4] [ ( 5 x + 3) – 4 ] Simplifying www. mathssupport. org [ 5 x + 7 ] [ 5 x – 1 ]
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