Expanding

Expanding single brackets

In expansion of single brackets term outside the bracket gets multiplied with all the terms inside the brackets.

Example : 8 ( a+ b)

Here `8` is first multiplied with the first term `a` and then second term `b` (8 x a + 8 x b) = 8a + 8b

Let`s consider other example -b (a+b).

Here `b` along with `-` sign will multiply with both the terms.

Thus equation will become (-b x a + - b x b ) = -ba - b² or -ab - b ²

Lets try the following expansion :

Solve (y+1) (y+2)

Here `y ` from the first bracket will multiply with all the terms in the second bracket and similarly `1` from the first bracket will multiply with all the terms in the second bracket.

Remember the sign conventions.

(y (y+2) +1 (y+1)) = y ² +2y+y+1 = y ²+3y+1

Next we are moving towards addition or subtraction in expansion.

Example : 5 (a+4) + 5 (a+6)

The method we apply is the same as normal expansion we had done before .

Solution for above is :

( 5 x a + 4 x 5 + 5 x a + 5 x 6) .

Bringing like terms together.

5a + 5a +20 +30 = 10a+50