Unit 2: Algebra
Use the rules of indices to simplify algebraic expressions
An index number, or a power, is the small floating number that goes next to a number or letter. The plural of index number is indices. Index numbersshow how many times a number or letter has been multiplied by itself.
To answer this question, write and out in full: and.
Writing the indices out in full shows that means has now been multiplied by itself 5 times. This means can be simplified to .
Expanding brackets involves removing the brackets from an expression by multiplying out the brackets.
Example 1 - Expanding a single pair of brackets
a) Expand: 3(x+6)3(x+6).
a) Remember to multiply every term inside the brackets by the term outside:
Example 2 - Expanding and simplifying brackets
a) Expand and simplify 2(3x+4)+4(x−1)2(3x+4)+4(x−1).
Multiply each bracket out first, then collect the like terms:
Example 3 - Expanding double brackets
Expand and simplify (a+b)(c+d)(a+b)(c+d).
When multiplying out double brackets, each terms in the first bracket must be multiplied by each term in the second:
Example 4 - Expanding and simplifying quadratic expressions
a) Expand and simplify (x+4)(x+3)(x+4)(x+3).
When multiplying xx by another xx you will end up with an x2x2 term:
Factorise algebraic expressions.
Factorise the expression: c2- 3c - 10
Write down the expression: c2- 3c - 10
Remember that to factorise an expression we need to look for common factor pairs. In this example we are looking for two numbers that:
- multiply to give -10
- add to give -3
Think of all the factor pairs of -10:
- 1 and -10
- -1 and 10
- 2 and -5
- -2 and 5
Which of these factor pairs can be added to get -3?
Only 2 + (-5) = -3
So the answer is:
c2 - 3c - 10 = (c + 2)(c - 5)
Factorising the difference of two squares
Factorise: x2 - 4
x2 - 4 = (x + 2)(x – 2)
Factorise: x2 -…