Squaring Out Brackets.

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

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 + y 2 = x 2 + 2xy + y 2 Key Result: (x + y ) 2 = x 2 + 2xy + y 2

How To Multiply Out A Square 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. x 2 (2) Take the product of the two terms and double them. 2xy (3) Square the second term. y 2 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) (2x + 3y) 2 = (1) Square out the first term. 4x 2 (2) Double the product of the terms. +12xy (3) Square out the last term. +9y 2 (2) (5x + 2y) 2 =25x 2 +20xy+4y 2 (1) Square out the first term. (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 (2) ( 2w + 5m) 2 (3) ( 6f + 3g) 2 (4) ( 7b + 6a) 2 (5) ( 9y + 9w) 2 = 16x 2 +24xy + 9y 2 = 4w 2 +20wm + 25m 2 = 36f 2 +36fg + 9g 2 = 49b 2 +84ab + 36a 2 = 81y yw + 81w 2

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 wt+ 36 t 2

What Goes In The Box ? 2 Multiply out the brackets below : (1) ( 4 w – 6 f ) 2 = (2) ( 7 r – 3 g ) 2 = (3) ( 5 t – 2 h ) 2 = (4) ( 9 d – 3 a ) 2 = 16w wf+36f 2 49r rg+9g 2 25t ht+4h 2 81d ad+9a 2