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1. Take out common factors

example: 3y+12

• 3y= 3 x y
• 12= 3 x 4
• both terms have the Highest Common Factor(HCF) 3

thus, 3y+12= 3(y+4)

2. Grouping the terms

10ax-35ay+8bx-28by= 5a(2x-7y)+ 4b(2x-7y)                                  =(5a+4b)(2x-7y)

a² - b² = (a+b)(a-b)

a² + 2ab + b² = (a+b)(a+b)

a² - 2ab + b² = (a-b)(a-b)

Methods:

1. a(b + c) = (ab + ac)

2. a² - b² = (a - b)(a + b)

3.(a - b)(a + b)= a²  - 2 ab + b²

(a+b)(x+y)= a(x+y)+ b(x+y)             

                 = ax+ay+bx+by

In Algebra putting two things next to each other usually means to multiply.

So 3(a+b) means to multiply 3 by (a+b)

  example: a(b+c)= ab+ac

So, to remove a set of brackets from an expression we multiply each term inside the brackets by the term in front of them. The resulting terms are then simplified.