Algebraic Expressions
1. Given a = -1, b = 2, c = -3, d = 2
Evaluate:
4ab ✕ 5ab2
d 3c2d2
Solution:
4ab ✕ 5ab2 = 4a2b3
d 3c2d2 3d3c2
4 ✕ (-1)2 ✕ (2)3 = 4 ✕ 1 ✕ 8 = 32
3 ✕ (2)3 ✕ (-3)2 3✕ 8✕ 9 219
32 = 4
216 27
2. Two consecutive even numbers are such that the difference of thrice the larger
number and twice the smaller number is equal to 17. Find the product of the
numbers.
Solution:
Let’s say the smaller number is x
Therefore, the larger number will be x + 2
Thrice the larger number is 3(x + 2)
Twice the smaller number is 2x
So, 3(x + 2) - 2x = 17
3x + 6 - 2x = 17
3x - 2x + 6 = 17
x = 17 - 6 (the sign changes after taking the +6 to the other side of the equal
sign)
x = 11
The two numbers are, therefore:
(Smaller) x = 11
(Larger) x + 2 = 13
1. Given a = -1, b = 2, c = -3, d = 2
Evaluate:
4ab ✕ 5ab2
d 3c2d2
Solution:
4ab ✕ 5ab2 = 4a2b3
d 3c2d2 3d3c2
4 ✕ (-1)2 ✕ (2)3 = 4 ✕ 1 ✕ 8 = 32
3 ✕ (2)3 ✕ (-3)2 3✕ 8✕ 9 219
32 = 4
216 27
2. Two consecutive even numbers are such that the difference of thrice the larger
number and twice the smaller number is equal to 17. Find the product of the
numbers.
Solution:
Let’s say the smaller number is x
Therefore, the larger number will be x + 2
Thrice the larger number is 3(x + 2)
Twice the smaller number is 2x
So, 3(x + 2) - 2x = 17
3x + 6 - 2x = 17
3x - 2x + 6 = 17
x = 17 - 6 (the sign changes after taking the +6 to the other side of the equal
sign)
x = 11
The two numbers are, therefore:
(Smaller) x = 11
(Larger) x + 2 = 13
