Page 44 - 新思维数学学生用书8 样章

2.3 Expanding brackets

6 Jing, Jun and Amira compare the methods they use to expand the bracket 5k(6m − 8k).

Jing uses the method shown in Jun uses a multiplication Amira uses multiplication arcs.

Question 3. box.
5k(6m – 8k) x 6m –8k
= 5k × 6m – 5k × 8k 5k 30km –40k 2 5k(6m – 8k) = 30km – 40k 2
= 30km – 40k 2 2
So 5k(6m – 8k) = So 5k(6m – 8k) = 30km – 40k
30km – 40k 2

a What do you think about Jing, Jun and Amira’s methods?
b Which method do you think is best for expanding brackets correctly? Explain why.

c Use your favourite method to expand
i 2x(x + 3y) ii 3y(5y + 6)
iii 4b(6b − 2a) iv 2f(2f + g − 3)
7 Here are some expression cards.

Sort the cards into groups of equivalent expressions.

8 (
3 (
A 2xx + 6x) B 10xx + ) C 2x ( 12x + ) Tip
2
2
2
2
9
x(
D 2 10 15x ) E 4x ( 4x + ) F 3x ( 68x) For card A,
2
2
2
+
+
3
2x(8x + 6x)
2
3
(
3 (
(
G 5 6x + 4x) H 6xx + 4x ) I x 12 16 ) = 16x + 12x 2
2
+
x
3
2
Think like a mathematician
8 Work with a partner to discuss this question.
Look at this expansion. x(2x + 5) + 3x(2x + 4) = 2x + 5x + 6x + 12x
2
2
a How would the expansion change if the + changed to −?
Here is the expansion again. x(2x + 5) + 3x(2x + 4) = 2x + 5x + 6x + 12x
2
2
b How would the expansion change if both the + changed to −?
c Copy these expansions and fill in the missing signs (+ or −).

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