Squaring Out Brackets.

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# Squaring Out Brackets. - PowerPoint PPT Presentation

Squaring Out Brackets. Squaring Out Brackets. Double Bracket Reminder. Multiply out the brackets below :. ( 2x + 4 ) ( 3x – 8 ). = 2x. ( 3x - 8 ). +4. ( 3x - 8 ). = 6x 2. -16x. +12x. -32. = 6x 2. -4x. -32. Multiplying Out (x + y ) 2.

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## Squaring Out Brackets.

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Squaring Out Brackets.

Double Bracket Reminder.

Multiply out the brackets below :

( 2x + 4 ) ( 3x – 8 )

= 2x

( 3x - 8 )

+4

( 3x - 8 )

= 6x2

-16x

+12x

-32

= 6x2

-4x

-32

Multiplying Out (x + y ) 2

Consider how to multiply out the brackets below:

(x + y ) 2

If 6 = 6 x 6 and 7 = 7 x 7 then …..

= ( x + y )( x + y )

= x

( x + y )

+ y

( x + y )

=

x 2

+ xy

+ xy

+ y 2

Key Result:

(x + y ) 2 = x 2 + 2xy + y 2

= x 2 + 2xy + y 2

How To Multiply Out ASquare Bracket.

(x + y ) 2 = x 2 + 2xy + y 2

The key result above gives us a shortcut method to square out any bracket. It tells us to do the following:

(1) Square the first term of our expression. x2

(2) Take the product of the two terms and double them. 2xy

(3) Square the second term . y2

By repeating these moves on any square bracket we can multiply out the bracket in one line.

Squaring Out Brackets.

Square out the bracket below :

(1) Square out the first term.

(1) (2x + 3y)2

(2) Double the product of the terms.

=

4x 2

+12xy

+9y2

(3) Square out the last term.

(2) (5x + 2y)2

(1) Square out the first term.

=

25x 2

+20xy

+4y2

(2) Double the product of the terms.

(3) Square out the last term.

What Goes In The Box ?

Multiply out the brackets below:

(1) ( 4x + 3y)2

= 16x 2

+24xy

+ 9y 2

(2) ( 2w + 5m) 2

= 4w 2

+20wm

+ 25m2

(3) ( 6f + 3g) 2

= 36f 2

+36fg

+ 9g 2

(4) ( 7b + 6a) 2

= 49b 2

+84ab

+ 36a 2

(5) ( 9y + 9w) 2

= 81y 2

+162yw

+ 81w2

Squaring Out Brackets With Negatives

Multiply out the bracket below which contain a negative sign :

( 4w – 6t ) 2

( 4w x 4w)

( 4w x – 6t )

(– 6t x – 6t)

=

+

+

16 w 2

- 24wt

+ 36 t 2

=

What Goes In The Box ? 2

Multiply out the brackets below :

(1) ( 4 w – 6 f )2 =

16w 2

- 48wf

+36f 2

(2) ( 7 r – 3 g )2 =

49r 2

- 42rg

+9g 2

25t 2

- 20ht

+4h 2

(3) ( 5 t – 2 h )2 =

81d 2