Question 1
LEVEL 3
From the answers below, choose the correct expansion of 3x(x + y).
A: 3x^2 + 3y^2
B: 3x^2 + y
C: 3x^2 + 3xy
D: 3x + 3y
CORRECT ANSWER: C: 3x^2 + 3xy
WORKED SOLUTION:
We must multiply the term in front of the bracket by both terms inside the bracket. So, we get
3x(x + y) = (3x \times x) + (3x \times y) = 3x^2 + 3xy.
Question 2
LEVEL 3
Which of the following four answers is the correct expansion of 4a(2 - a + ab)?
A: 8a - 4a^2 + 4ab
B: 8a - 4a + 4ab
C: 8a - 4a^{3}b
D: 8a - 4a^2 + 4a^{2}b
CORRECT ANSWER: D: 8a - 4a^2 + 4a^{2}b
WORKED SOLUTION:
We must multiply the term in the front of the bracket by all 3 terms inside the bracket. So, we get
4a(2 - a + ab)
= (4a \times 2) + (4a \times -a) + (4a \times ab)
= 8a - 4a^2 + 4a^{2}b.
Question 3
LEVEL 3
Expand the following:
4(2a+2)Select the correct answer from the list below:
A: 4a+4
B: 8a + a
C: 8a+8
D: 8a^2
CORRECT ANSWER: C: 8a+8
WORKED SOLUTION:
We must multiply the term in the front of the bracket by both terms inside the bracket. So, we get
(4 \times 2a) + (4 \times 2)= 8a + 8.
Question 4
LEVEL 3
Expand the following:
5h(3h+3a)Select the correct answer from the list below:
A: 15h+3a
B: 15h^2 + 15ah
C: 15h^2 + 15a
D: 15g^2 + 15ha
CORRECT ANSWER: B: 15h^2 + 15ah
WORKED SOLUTION:
We must multiply the term in the front of the bracket by both terms inside the bracket. So, we get
(5h \times 3h) + (5h \times 3a)= 15h^2 + 15ah
Question 5
LEVEL 3
Expand and simplify the following:
5(2a+3b) - 2(a+b)Select the correct answer from the list below:
A: -8a+13b
B: 12a+17b
C: 8a-13b
D:8a+13b
CORRECT ANSWER: D:8a+13b
WORKED SOLUTION:
We must multiply the term in the front of the first bracket by both terms inside the bracket. So, we get
(5 \times 2a) + (5 \times 3b) = 10a + 15b
Then we need to do the same to the second bracket. So, we get
(-2 \times a) + (-2 \times b) = -2a - 2b
Then you bring like terms together to complete the expansion
8a+13b