Algebra 1 + 2

Question 1

Factorising using common factors

Answer 1

For example, 4x* + 10xy ( * = Squared) can be factorised into 2x ( 2x + 5y ) as 2x is in both 4x* and 10xy

Question 2

Factorising using Quadratics

Answer 2

For example, x* + 4x - 32 can be factorised to ( x + 8 )( x - 4 ) using reversed foil ( Horseshoe ). If - is at the end, the order of + or minus is + -, if + is at the end, whatever is at the start, wether it is + or -, it will be 2 of that symbol. For example if it is x* - 11x + 18 is factorised to ( x - 2 )( x - 9 ).

Question 3

Factorising with Harder Quadratics

Answer 3

For example, 3x* - 17x + 10 is factorised to ( x - 5 )(3x-2). As there is a 3x, it may be hard to piece together the right order of the x and + numbers so keep trying until something fits!

Question 4

Factorising using D.O.T.S ( Difference Of Two Squares )

Answer 4

If you get a question like x* - 64, you are supposed to factorise both numbers to their square roots. For example 4x* - 25 can be factorised to ( 2x + 5 )( 2x - 5 ).

Question 5

Simplifying algebraic expressions

Answer 5

For example, 2y - 3x + 5 + 5y + 2x +1 can be factorised to the equation 7y - x + 6 by adding the X’s together and adding the Y’s together. Once this is done just add the other numbers together and you should be done!

Question 6

Expanding Brackets

Answer 6

For Example, 2 ( 2x - 1) can be expanded to 4x - 2 if you times 2x and 1 by 2 as it is on the outside of the bracket. Another example is: 5 - 2 ( x + 9 ) can be expanded to -2x - 13

Question 7

Using F.O.I.L (Firsts, Outers, Inners, Lasts)

Answer 7

For Example, ( 2x + 1 )( 3x - 5 ) can be expanded to 6x* - 7x - 5 by multiplying the firsts together , multiplying the outers together, multiplying the inners together and multiplying the lasts together. Once that is done add the outers and inners together and there you go!

Question 8

Algebraic Identities

Answer 8

For Example, If ax* + bx + c = ( 5x + 1 ), we can find A, B & C by comparing the 2 sides. In this example, A = 25, B = 10 & C = 1. We can find this out by expanding ( 5x + 1 ) to 25x* + 10x + 1 which leaves you with ax* + bx + c = 25x* + 10x + 1. You then compare them and realise that ax* must be 25x* and that bx must be 10x resulting in A = 25, B = 10 & C = 1

Question 9

Solving Linear Equations

Answer 9

For Example, 3w + 6 - w = 1 + w can be simplified to the equation 2w + 6 = 1 + w. You then swap around the 6 and w to get 2w - w = 1 - 6 which leaves you with w = -5