Squaring Out Brackets Double Bracket Reminder Multiply out

Squaring Out Brackets.

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

Multiplying Out (x + y ) 2 Consider how to multiply out the brackets below: (x + y ) 2 = ( x + y ) If 6 = 6 x 6 and 7 = 7 x 7 then …. . =x (x+y) +y (x+y) = x 2 + xy + y 2 Key Result: = x 2 + 2 xy + y 2 (x + y ) 2 = x 2 + 2 xy + y 2

How To Multiply Out A Square Bracket. (x + y ) 2 = x 2 + 2 xy + 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. (3) Square the second term. y 2 By repeating these moves on any square bracket we can multiply out the bracket in one line. 2 xy

Squaring Out Brackets. Square out the bracket below : (1) Square out the first term. (2 x + 3 y)2 = 4 x +12 xy +9 y 2 2 (2) Double the product of the terms. (3) Square out the last term. (2) (5 x + 2 y)2 = 25 x 2 +20 xy +4 y 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: = 16 x 2 +24 xy + 9 y 2 (2) ( 2 w + 5 m) 2 = 4 w 2 +20 wm + 25 m 2 (3) ( 6 f + 3 g) 2 = 36 f 2 +36 fg + 9 g 2 (4) ( 7 b + 6 a) 2 = 49 b 2 +84 ab (5) ( 9 y + 9 w) 2 = 81 y 2 (1) ( 4 x + 3 y)2 + 36 a 2 +162 yw + 81 w 2

Squaring Out Brackets With Negatives Multiply out the bracket below which contain a negative sign : ( 4 w – 6 t ) 2 = = ( 4 w x 4 w) + ( 4 w x – 6 t ) 16 w 2 - 24 wt + 36 t 2 + (– 6 t x – 6 t)

What Goes In The Box ? 2 Multiply out the brackets below : (1) ( 4 w – 6 f )2 = 16 w 2 - 48 wf +36 f 2 (2) ( 7 r – 3 g )2 = 49 r 2 - 42 rg +9 g 2 = 25 t 2 - 20 ht +4 h 2 = 81 d 2 - 54 ad +9 a 2 (3) ( 5 t – 2 h )2 (4) ( 9 d – 3 a )2