# A4L simplify expand factorise - Web Maths_ Ashlawn School

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1 simplify by collecting like terms with one letter only

2 simplify by collecting like terms with multiple letters and numbers

3 simplify by multiplying numbers and letters together

4 simplify by using the basic rules of indices for multiply, divide and brackets

5 simplify expressions in brackets with powers

6 expand single brackets by a whole number

7 expand single brackets by numbers and letters

8 expand double brackets of the type (x±a)(x±b)

9 expand double brackets of the type (ax±b)(cx±d)

10 expand double brackets of the type (ax±b)²

11 factorise simple expressions

12 factorise more complex expressions

13 factorise quadratics of the type x²+bx+c into 2 brackets

14 factorise quadratics of the type ax²+bx+c into 2 brackets

15 factorise quadratics of the type x² - a² into 2 brackets by using the difference of 2 squares
How to                                                    Q1        Q2         Q3
look carefully at the signs and add or subtract as
appropriate                                               5a + 2a   6a - 4a    3a + 2a - a
put the same letters in columns and add or subtract as
appropriate                                                         6a + 5      +8
5a + 2b + 3a + 7b- 2a5y - 1 - 2y + 8
multiply the numbers and then the letters. Remember
that we do not use x signs between numbers and letters
in algebra.                                               3a x 2b              5a
2c x 5d x 4e x 2a

add the powers when multiplying, subtract the powers
when dividing and multiply the powers in brackets         y³ x y²   h² ÷ h³    (a³)³
raise every number and letter to the power outside the
bracket                                                   (2xy²)²   (5a²b)³    (3x³y²)³
use the grid method and multiply the terms by the
number outside the bracket                                5(a+7)    3(b-4)     4(5y+2)
use the grid method and multiply the terms by the
number and letter outside the bracket                     2a(a+6)   5b(3b-1) 3a²(4a+7)
use the grid method and think carefully about the signs
when you are multiplying and adding                       (x+7)(x+5)(x-3)(x+5) (x+9)(x-2)
use the grid method and think carefully about the signs
when you are multiplying and adding                                 (5x-1)(2x+7)
(2x+3)(x+4)         (3x+4)(3x-4)
use the grid method and remember that you need a
double grid.                                              (x+5)²    (x-9)²     (2x+3)²
use the BIG F method and take out the highest common
factor                                                    3y + 15   4h - 10    24a + 40b
use the BIG F method and take out the highest common
factors                                                   3y²+6y    4ab - 16b²20a²b³+35ab²
find 2 numbers that Add to make the middle term and
Times to make the end term. Remember AT.                                        x²
x² + 5x + 6x² + 2x - 15 - 3x - 40
find the 2 numbers that multiply to make the first term
and multiply to make the end term. Then check to
make sure the middle term is correct.                                20          16
2x² + 9x + 3x² + 22x -5x² - 31x - 28
spot the squares in the first and second terms then use
the form (x+a)(x-a)                                       x² - 9    x² - 100   4x² - 25
Q4

5a - 3a + 2a - 10a

8a + 2b - 3 -5b + 2a + 7

3h² x 2g³ x 4h³ x g

(v³ x v³)²

(8b³cd²)²

7(3d+2f-4h)

4y²(5y³-7)

(x-6)(x-3)

(2x-5)(3x-1)

(3x-1)²

9a+12b-18

15ab²-10ab+45ab³

x² - 14x + 48

4x² - 20x + 21

16x² - 81y²
Comment

To improve you need to be able to simplify by collecting like terms with one
1                                              letter only
1   To be able to do this you must remember to

1 look carefully at the signs and add or subtract as appropriate
1 5a + 2a                                          6a - 4a
1 3a + 2a - a                                      5a - 3a + 2a - 10a
Have you now achieved this target?
Comment

To improve you need to be able to simplify by collecting like terms with one
1                                              letter only
1   To be able to do this you must remember to

1 look carefully at the signs and add or subtract as appropriate
1 5a + 2a                                          6a - 4a
1 3a + 2a - a                                      5a - 3a + 2a - 10a
Have you now achieved this target?

Comment

To improve you need to be able to simplify by collecting like terms with one
1                                              letter only
1   To be able to do this you must remember to

1 look carefully at the signs and add or subtract as appropriate
1 5a + 2a                                          6a - 4a
1 3a + 2a - a                                      5a - 3a + 2a - 10a
Have you now achieved this target?

Comment

To improve you need to be able to simplify by collecting like terms with one
1                                              letter only
1   To be able to do this you must remember to

1 look carefully at the signs and add or subtract as appropriate