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ALGEBRA : Multiplying out double brackets
Multiply out these brackets and simplify where possible.
( n + 9 )( n - 2 ) =
( t - 4 )( t + 5 ) =
( x + 8 )( x + 1 ) =
( x - 3 )( x - 6 ) =
( y - 7 )( y + 7 ) =
( 5 + t )( 3 - t ) =
( x - 4 )² =
( x - 1 )( 2x + 3 ) =
( a - 2b )( a + 3b ) =
Work out the missing term :
( x + 3 )( x + 5 ) = x² ______________ + 15
( n - 4 )( n + 1 ) = n² ______________ - 4
( x - 5 )( x - 10 ) = x² ______________ + 50
( a + 5 )² = a² ______________ + 25
Work out the missing factor :-
x² + 13x + 30 = ( x + 10 )( )
n² - 4n - 21 = ( n - 7 )( )
y² - 14y + 49 = ( y - 7 )( )
x² - 16 = ( x - 4 )( )
t² - 4t - 45 = ( )( t + 5 )
2x² + 5x + 3 = ( x + 1 )( )
6n² + 3n - 18 = 3 ( )
ALGEBRA : Factorising Quadratics
If you multiply out ( x + 6 )( x + 3 ) you get x² + 9x + 18
To factorise x² - 7x + 10 you have to find two numbers that
multiply to give + 10 and add up to -7
-1 + -10 = -11 x
-2 + -5 = -7 works
So x² - 7x + 10 = ( x - 2 )( x - 5 )
To factorise x² + 5x + 6, ( x + 2 )( x + 3 ) and ( x + 1 )( x + 6 ) both
multiply out to give the x² and the + 6 but which one will give + 5x ?
x² + 5x + 6 =
Which one of these is the correct factorisation of x² + 2x - 8 ?
( x - 1 )( x + 8 ) =
( x + 1 )( x - 8 ) =
( x - 2 )( x + 4 ) =
( x + 2 )( x - 4 ) =
Which one of these is the correct factorisation of x² - x - 12 ?
( x - 1 )( x + 12 ) ( x + 1 )( x - 12 )
( x - 2 )( x + 6 ) ( x + 2 )( x - 6 )
( x - 3 )( x + 4 ) ( x + 3 )( x - 4 )
ALGEBRA : Factorising Quadratics 6 + 3 6 x 3
Both numbers haveto be negative.
You have to find which oneswork by trying them out !
Factorise these quadratic expressions
x² + 8x + 15 =
x² + 9x + 14 =
t² - 8t + 12 =
x² + 5x + 4 =
n² - 12n + 36 =
n² - 4n - 21 =
y² + 3y - 10 =
y² - 10y + 25 =
a² - a - 2 =
x² - 36 =
z² + 3z - 40 =
Factorise out the common factor first then factorise the quadratic expression :
2x² + 6x + 4 =
5x² - 10x - 15 =
ALGEBRA : Factorising Quadratics
Factorize the following expressions using DOTS (Difference of Two Squares):
1. 25m2 − 49
2. 36 − 81b2
3. 6w2− 600
4. 48x2 − 75
Remember, always look for HCF first!
5. (x + 4)2 − 9
6. (p − 11)2 − 81
7. 64 − (v + 7)2
8. (5w − 7)2 − 9w2
9. (3x + 2y)2−(x + y)2
10. (4p +5q)2 − (2p − 3q)2
Sove these quadratic equations :
n² - 3n - 10 = 0
x² - 18x + 81 = 0
0 = y² + 5y + 6
8 - 6x + x² = 0
a² + 3a - 40 = 0
0 = x² + 19x - 42
z² = 45 + 12z
ALGEBRA : Solving Quadratic Equations
ALGEBRA : Solving Harder Quadratic Equations
x² - 9 = 0
n² - 4n = 0
t² = 16t
150y = 6y²
2a² + 7a + 3 = 0
3x² + 2x - 1 = 0
6n² + n - 2 = 0
ALGEBRA : Solving Harder Quadratic Equations
36 - k² = 0
7b - b² = 0
49t = t²
4x² = 25
2a² + 5a + 2 = 0
5x² - 3x - 2 = 0
8n² + 19n - 15 = 0
The length of this rectangle is 4 metres more than the width which is x metres.
The area of the rectangle is 45 m².
[1] Show that x² + 4x - 45 = 0
[2] Solve the equation x² + 4x - 45 = 0
[3] What is the value of x ?
x metres
The widtth of this rectangle is 6 metres less than the length which is x metres.
The area of the rectangle is 55 m².
[1] Show that x² - 6x - 55 = 0
[2] Solve the equation x² - 6x - 55 = 0
[3] What is the value of x ?
x metres
The area of this shape is 36 cm².
[1] Show that x² + 7x - 18 = 0
[2] Solve the equation x² + 7x - 18 = 0
[3] What is the value of x ?
2x cm
x cm
x + 14 cm
2x + 3 cm
x cm
x + 7 cm
[1] Show that x² - x - 20 = 0
[2] Solve the equation x² - x - 20 = 0
[3] What is the value of x ?
ALGEBRA : Multiplying out double brackets
Multiply out these brackets and simplify where possible.
( 2n + 3 )( n + 1 ) =
( t - 2 )( 3t + 5 ) =
( 5x + 3 )( x + 1 ) =
( 2x - 3 )( 2x - 1 ) =
( 3y - 4 )( 3y + 4 ) =
( 1 + 3t )( 3 - t ) =
( 3x - 4 )² = _
( 5x - 1 )( 2x + 3 ) =
( 3a - 2b )( 2a + 3b ) = _
Work out the missing term :
( 2x + 5 )( x + 2 ) = 2x² ______________ + 10
( n - 3 )( 3n + 1 ) = 3n² ______________ - 3
( 5x - 3 )( x - 2 ) = 5x² ______________ + 6
( 2a + 5 )² = 4a² ______________ + 25
Work out the missing factor :
2x² + 11x + 15 = ( x + 3 )( )
3n² - n - 2 = ( 3n + 2 )( )
3y² - 11y + 6 = ( 3y - 2 )( )
4x² - 25 = ( 2x - 5 )( )
4t² - 2t - 12 = ( )( 2t + 3 )
5x² + 22x + 8 = ( x + 4 )( )
2n² + 5n - 12 = ( 2n - 3 )( )
ALGEBRA : Factorising Quadratics
ALGEBRA : Factorising Quadratics
Factorise these quadratic expressions
2x² + 5x + 3 = _________________________________________________
3x² + 19x + 6 =
2t² - 11t + 5 =
2x² + 9x + 10 =
3n² - 10n + 8 =
ALGEBRA : Factorising Quadratics
Factorise these quadratic expressions
5n² + 13n + 6 = _________________________________________________
2y² + 2y - 4 = _________________________________________________
5y² - 13y + 6 = _________________________________________________
5a² - 6a + 1 = _________________________________________________
7z² + 15z + 2 = _________________________________________________
ALGEBRA : Solving Harder Quadratic Equations
Solve these quadratic equations :
2n² + 13n + 20 = 0
2y² - 17y + 8 = 0
21y = 5y² + 4
3a² + 14a = 5
ALGEBRA : Solving Harder Quadratic Equations
Solve these quadratic equations :
2n² - 5n - 12 = 0
3y² - 16y + 5 = 0
11y = 7y² + 4
4a² - 16a + 15 = 0
