Solve the following by expanding brackets 16 multply 110
Answers
Answer:
Expanding brackets
and simplifying expressions
A LEVEL LINKS
Scheme of work: 1a. Algebraic expressions – basic algebraic manipulation, indices and surds
Key points
• When you expand one set of brackets you must multiply everything inside the bracket by
what is outside.
• When you expand two linear expressions, each with two terms of the form ax + b, where
a ≠ 0 and b ≠ 0, you create four terms. Two of these can usually be simplified by collecting
like terms.
Examples
Example 1 Expand 4(3x − 2)
4(3x − 2) = 12x − 8 Multiply everything inside the bracket
by the 4 outside the bracket
Example 2 Expand and simplify 3(x + 5) − 4(2x + 3)
3(x + 5) − 4(2x + 3)
= 3x + 15 − 8x – 12
= 3 − 5x
1 Expand each set of brackets
separately by multiplying (x + 5) by
3 and (2x + 3) by −4
2 Simplify by collecting like terms:
3x − 8x = −5x and 15 − 12 = 3
Example 3 Expand and simplify (x + 3)(x + 2)
(x + 3)(x + 2)
= x(x + 2) + 3(x + 2)
= x2 + 2x + 3x + 6
= x2 + 5x + 6
1 Expand the brackets by multiplying
(x + 2) by x and (x + 2) by 3
2 Simplify by collecting like terms:
2x + 3x = 5x
Example 4 Expand and simplify (x − 5)(2x + 3)
(x − 5)(2x + 3)
= x(2x + 3) − 5(2x + 3)
= 2x2 + 3x − 10x − 15
= 2x2 − 7x − 15
1 Expand the brackets by multiplying
(2x + 3) by x and (2x + 3) by −5
2 Simplify by collecting
Step-by-step explanation: