Skills&Worksheet&–&Expanding&Double&Brackets&

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Expand!&!Simplify!Double!Brackets!!1.! Work!out!the!following:!! a)! 7!×!3! ! ! c)! −6!×!10!! b)! 2!×!−8!! ! d)! −4!×!−9!! !2.!! Simplify!the!following!expressions:!

a)! !!×!!! ! ! c)! −6!×!!!b)! 5!×!!! ! ! d)! 3!×!−!!

!3.! Expand:!

a)! !(! + 2)! ! c)! 5(! + 8)! ! e)! !(! + ℎ)! !b)! !(! − 6)! ! d)! 7(! − 4)! ! f)! !(! − !)! !

!4.! Expand!and!simplify!the!following:!

a)! (! + 3)(! + 5)!! ! d)! (! + 9)(! + 11)!b)! (! + 10)(! + 2)! ! e)! (! + !)(! + !)!c)! (! + 6)(! + 3)!! ! f)! ! + 1 !!

!5.!! Expand!and!simplify!the!following:!! a)! (! − 3)(! − 2)!! ! d)! (! − 11)(! − 1)!

b)! (! − 7)(! − 5)!! ! e)! (! − !)(! − !)!c)! (! − 9)(! − 10)! ! f)! ! − 5 !!

!6.!! Expand!and!simplify!the!following:!! a)! (! + 6)(! − 2)!! ! d)! (! − 9)(! + 10)!

b)! (! − 10)(! + 4)! ! e)! (! + !)(! − !)!c)! (! + 8)(! − 6)!! ! f)! (! + 3)(! − 3)!

!7.!! Expand!and!simplify!the!following:!! a)! (! − 3)(! − 8)!! ! d)! (! − 4)(! + 10)!

b)! (! + 5)(! + 8)! ! ! e)! (! − 100)(! − 10)!c)! (! + 11)(! − 2)! ! f)! (! + 20)(! − 2)!!

8.! Write!an!expression!for!the!area!of!the!rectangle!shown!below.!!Your!answer!should!have!no!brackets!in!it.!

!

!!!!!9.! Jessica!has!tried!to!answer!a!question!below!but!has!made!at#least#3#different!mistakes.!

Try!to$explain!to!Jessica!all!the!mistakes!she!has!made!and!what!she!should!have!done!instead.!

!! !

(! + 8)!!

(! − 2)!!

Expand$and$simplify$(! + !)(! − !)$

x2!-!4x!+!2x!+8 x2!-!6x!+!8 x2!+ 2x

!

Skills&Worksheet&–&Expanding&Double&Brackets&

! ! teemaths.com!

Expand!&!Simplify!Double!Brackets!<!SOLUTIONS!! !1.! a)! 21! ! ! c)! −60!! b)! −16! ! ! d)! 36!! !2.! a)! !!! ! ! c)! −6!!

b)! 5!! ! ! d)! −3!!!3.! a)! !! + 2!! ! c)! 5! + 40!! e)! !! + !ℎ! !

b)! !! − 6!! ! d)! 7! − 28! f)! !! − !!! !!4.! a)! !! + 8! + 15! ! ! d)! !! + 20! + 99!

b)! !! + 12! + 20! ! ! e)! !! + 2!" + !!!c)! !! + 9! + 18! ! ! f)! !! + 2! + 1!

!5.! a)! !! − 5! + 6! ! ! d)! !! − 12! + 11!

b)! !! − 12! + 35! ! ! e)! !! − 2!" + !!!c)! !! − 19! + 90! ! ! f)! !! − 10! + 25!

!6.! a)! !! + 4! − 12! ! ! d)! !! + ! − 90!

b)! !! − 6! − 40! ! ! e)! !! − !!!c)! !! + 2! − 48! ! ! f)! !! − 9!

!7.! a)! !! − 11! + 24! ! ! d)! !! + 6! − 40!

b)! !! + 13! + 40! ! ! e)! !! − 110! + 1000!c)! !! + 9! − 22! ! ! f)! !! + 18! − 40!!

8.! ! − 2 ! + 8 = !! + 6! − 16!!9.! +2 × −4 = −8!not!+8!!! −4! + 2! = −2!!not!−6x!!! −6! + 8!cannot!be!simplified!!! (There!are!other!‘mistakes’!too!that!follow!on!from!these)!