Algebra 3

The expression xy means x times y. But what are we to make of the expression x(y+1)? This must mean x times (y+1) which, in turn, means x times y plus x times 1 - everything outside the bracket is multiplied by everything inside the bracket. If you don``t think this sounds right put in some real values for x and y. For example if x=4 and y=3 then
xy = 4 times 3 = 12
and
x(y+1) = 4 times 4 = 16
or, multiplying everything outside the bracket by everything inside the bracket in turn,
x(y+1) = 4 times 3 plus 4 times 1 = 12 + 4 = 16.

Example 1
Expand s(2 + t)
Solution: s(2 + t) = s x 2 + s x t = 2s + st
Example 2 (Foundation May 15 Paper 2 Q14(b) )
Simplify 3(4a - 2c) - 2(2a+4c)
Solution: Multiply each term outside the bracket by each term inside the bracket. Do this for each bracket. We get 3(4a - 2c) - 2(2a + 4c) = 12a - 6c - 4a - 8c = 8a -14c
Example 3 (Foundation June 14 Paper 1 Q18(b) )
Expand y(y2 + 4) (Answer y3 + 4y)
Example 4 (Foundation Nov 15 Paper 2 Q15(a) )
Expand 5y(2y2 - 3). (Answer 10y3 -15y)
Example 5 (Foundation Nov 12 Paper 1 Q13(c) )
Expand 2x(x3+ 6). (Answer 2x4 +12x)
Example 6
Simplify 3y(x + 3) - 2x(y + 1) - xy - 9y (Answer -2x)
Example
Expand 2a(3a - b) + 2ab (Answer 6a2 )
Example 8
Simplify 3w(x - 2w + z) + 2x(z - w) - 2zx - 3wz (Answer wx - 6w2 )