Expanding Brackets
Information about Expanding
3(x + y) is 3 lots of (x + y)
Or
(x + y) + (x + y) + (x + y) = 3x + 3y
Can you see a quicker way of working it out?
5(3m – 4n) is 5 lots of (3m – 4n)
Or
(3m – 4n) + (3m – 4n) + (3m – 4n) + (3m – 4n) +( 3m – 4n) = 15m - 20n
Can you see a quicker way of working it out?
2t(4t + 7) is 2t lots of (4t + 7)
Crab’s
Claw?
Or
(2 x t x 4 x t) + (2 x t x 7) = 8t2 + 14t
Everything inside the bracket has to be multiplied by the term outside the bracket
4a3(3a2 + 2a)
(4 x a3 x 3 x a2) + (4 x a3 x 2 x a) = 12a5 + 8a4
Or
(4 x 3 x a3 x a2) + (4 x 2 x a3 x a) = 12a5 + 8a4
You will need to use your knowledge of multiplying indices here
Name:……………………………………………………….
Starter and Notes
Expand these Brackets
1) 2(r + t)
2) 7(e – d)
3) a(b – c)
4) 6(4p + 4)
5) -3(4r + 2w)
6) 9(4d – 3r)
7) 4r(6 + 2r)
8) -2a(4b – 3)
9) 6j(3k + 8h)
10) -8h(-2h – 4j)
11) 2ab (5a2 – 4b3)
12) 3y3 (2y9 + 3k12)
13) 5a3 (6a12 - t4)
14) 3r4t2 (4t + 2r7)
15) (6 - c)2
16) 9y3p2 (8y7 – 6p)
17) 2t3 (10r-1 + t8 + 5)
18) (5 + w)-3
Working out Section
Evaluation of Learning
Circle how confident are you at Expanding
Brackets?
(5 the highest)
1
2
3
4
If you circled 3 or below, try these
4 (3r + d)
7y (2 + 3y)
3k (k – 6n)
If you circled 4 or 5, try these
-12m(4m – 2h)
6a2b3 (3a4 + 5b8)
(b+3)2
5
Expanding with two brackets
2(a+4) + 3(a+5)
Treat it like two separate questions
2(a+4) = 2a+8
3(a+5) = 3a+15
Watch out
for
multiplying
negatives!
Then simplify  5a+23
4(b+4) – 2(b-3)
Treat like two separate questions
4(b+4) = 4b+16
-2(b-3) = -2b+6
Then simplify  2b+22
Expand and simplify
1) 2(w+7) + 4(w+2)
5) 3(t+5) – 2(t+1)
2) 5(p+3) + 2(p+1)
6) 4(x-3) – 5(x-4)
3) 7(m-3) + 3(m+5)
7) 2(x-9) – 8(x-7)
4) 6(b+6) + 5(b-4)
Grade C
Expanding Double Brackets
Crabs Claw
Watch out
for
multiplying
negatives!
(y+2)(y+3)
y x y = y2
y x 3 = 3y
2 x y = 2y
2x3=6
Then simplify y2 + 5y + 6
Grid Multiplication
(y-3)(y+4)
y
4
y
y2
4y
-3
-3y
-12
Then simplify y2 + y -12
Expand and Simplify
1)
(x+4)(x+5)
2)
(w+7)(w+3)
3)
(p+2)(p-4)
4)
(t-3)(t+2)
5)
(y-6)(y-6)
6)
(m-5)(m+10)
7)
(n+4)2