Question 1-3 : Simplify the algebraic expression.
Question 1 :
Answer :
Question 2 :
4x^{3} - 2(x^{3} + 3x)
Answer :
= 4x^{3} - 2(x^{3} + 3x)
= 4x^{3} - 2x^{3} - 6x
= 2x^{3} - 6x
Question 3 :
a(2 - b) - 2(a - b)
Answer :
= a(2 - b) - 2(a - b)
= 2a - ab - 2a + 2b
= -ab + 2b
Question 4 :
Which of the following expressions is equivalent to
(A) a^{2}
(B) a^{2} + a
(C) a^{2} - a
(D) a^{2} - 1
Answer :
= a^{2}
The correct answer is option (A).
Question 5 :
Which of the following expressions is equivalent to
5.4(x - 2y) - 2.7(x - 3y)
(A) 2.7(x + y)
(B) 2.7(x - y)
(C) 2.7x + 3.6y
(D) 2.7x - 3.6y
Answer :
= 5.4(x - 2y) - 2.7(x - 3y)
= 5.4x - 10.8y - 2.7x + 8.1y
= 2.7x - 2.7y
= 2.7( x- y)
The correct answer is option (B).
Question 6 :
Which of the following expressions is equivalent to
(A) a - 3c
(B) a + 5c
(C) a + c
(D) a - c
Answer :
= a - c
The correct answer is option (D).
Question 7 :
Which of the following expressions is equivalent to
a(b - c) - b(a + c) - c(a - b)
(A) bc
(B) 2ac
(C) -2bc
(D) -2ac
Answer :
= a(b - c) - b(a + c) - c(a - b)
= ab - ac - ab - bc - ac + bc
= -2ac
The correct answer is option (D).
Question 8 :
Which of the following expressions is NOT equivalent to
3a + 0.5(b - 2c) - 0.5(2a + 3b)
(A) 1.5a - 0.5b - c
(B) 1.5a + b - c
(C) 2a - b - c
(D) 2a + b - c
Answer :
= 3a + 0.5(b - 2c) - 0.5(2a + 3b)
= 3a + 0.5b - c - a - 1.5b
= 2a - b - c
The correct answer is option (C).
Question 9 :
Which of the following expressions is NOT equivalent to
3[6a - 3(1 - a) - 5(a + 1)]
(A) 12a - 24
(B) 24(a - 0.5)
(C) 12(a - 2)
(D) 24(0.5a - 1)
Answer :
= 3[6a - 3(1 - a) - 5(a + 1)]
= 3[6a - 3 + 3a - 5a - 5]
= 3(4a - 8)
= 12a - 24
Option (A) :
12a - 24
The is exactly the same as the simplified form of the given expression.
Option (B) :
= 24(a - 0.5)
= 24a - 12
This is NOT equivalent to the simplified form of the given expression.
Option (C) :
= 12(a - 2)
= 12a - 24
The is exactly the same as the simplified form of the given expression.
Option (D) :
= 24(0.5a - 1)
= 12a - 24
The is exactly the same as the simplified form of the given expression.
The correct answer is option (B).
Question 10 :
Which of the following expressions is NOT equivalent to
Answer :
Option (A) :
The is exactly the same as the simplified form of the given expression.
Option (B) :
The is exactly the same as the simplified form of the given expression.
Option (C) :
This is NOT equivalent to the simplified form of the given expression.
Option (D) :
The is exactly the same as the simplified form of the given expression.
The correct answer is option (C).
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