SAT MATH - SIMPLIFYING ALGEBRAIC EXPRESSIONS

Question 1-3 : Simplify the algebraic expression.

Question 1 :

Answer :

Question 2 :

4x3 - 2(x3 + 3x)

Answer :

= 4x3 - 2(x3 + 3x)

= 4x3 - 2x3 - 6x

= 2x3 - 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)  a2

(B)  a2 + a

(C)  a2 - a

(D)  a2 - 1

Answer :

= a2

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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