Algebra Questions and Answers

Q: Product of 4 and -3b is

\[ 4 \times (-3b) = -12b \]A positive times a negative is negative, and the numbers multiply as 4 and 3 to give 12.

Q: On evaluating algebraic expression -3(4s - 2t) - 4(2s + 3t), answer will be

Expand both brackets, distributing the negative signs.\[ -3(4s - 2t) = -12s + 6t \]\[ -4(2s + 3t) = -8s - 12t \]\[ (-12s - 8s) + (6t - 12t) = -20s - 6t \]The \( -3 \) turns \( -2t \) into \( +6t \), which is the sign most often lost.

Q: Sum of 5x + 3y and 4x - 2y is

Add like terms.\[ (5x + 3y) + (4x - 2y) = (5x + 4x) + (3y - 2y) \]\[ = 9x + y \]The \( y \) terms leave a coefficient of 1, which is written without the digit.

Q: If a = 20, b = 35 and c = 5 then (4a + b) / c is

Substitute and work through the numerator first.\[ 4a + b = 4(20) + 35 = 80 + 35 = 115 \]\[ \frac{115}{c} = \frac{115}{5} = 23 \]The whole numerator is divided by \( c \), not just the \( b \) - the 115 on offer is what you get by stopping one step early.

Q: Factorization of p(4q + 3) +4(4q+3) leads to

Both terms share the bracket \( (4q + 3) \).\[ p(4q+3) + 4(4q+3) = (p + 4)(4q + 3) \]Checking: \( 4pq + 3p + 16q + 12 \), which is what the original expands to.

Q: Algebraic form of product of 7y and 4z is

\[ 7y \times 4z = (7 \times 4)(y \times z) = 28yz \]The coefficients multiply and the variables are written side by side. Adding them instead would give \( 11yz \) - the first option.

Q: By factorizing \( 3x - 9y - 12z \), the answer will be

Each term is divisible by 3, so take it out.\[ 3x - 9y - 12z = 3(x - 3y - 4z) \]Both signs inside stay negative, since dividing \( -9y \) and \( -12z \) by \( +3 \) leaves them negative.

Q: In value 200x, variable is

In \( 200x \), the number 200 is the coefficient - a fixed value - while \( x \) is the variable, the symbol that can take different values.Anything expressed purely in numbers, such as \( 10(20) \), is a constant.

Q: By solving expression 4[3s - 2(6s - 8)], answer will be

Work from the inside out.\[ 2(6s - 8) = 12s - 16 \]\[ 3s - (12s - 16) = 3s - 12s + 16 = -9s + 16 \]\[ 4(-9s + 16) = -36s + 64 \]The minus in front of the inner bracket flips both its terms, turning \( -16 \) into \( +16 \).

Important Instructions

131.

Product of 4 and -3b is

A.12b
B.−12b
C.3b
D.−3b

Answer: B

\[ 4 \times (-3b) = -12b \]

A positive times a negative is negative, and the numbers multiply as 4 and 3 to give 12.

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132.

On evaluating algebraic expression -3(4s - 2t) - 4(2s + 3t), answer will be

A.−20s - 6t
B.−6s + 20t
C.21s - 7t
D.23s + 8t

Answer: A

Expand both brackets, distributing the negative signs.

\[ -3(4s - 2t) = -12s + 6t \]

\[ -4(2s + 3t) = -8s - 12t \]

\[ (-12s - 8s) + (6t - 12t) = -20s - 6t \]

The \( -3 \) turns \( -2t \) into \( +6t \), which is the sign most often lost.

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133.

Sum of 5x + 3y and 4x - 2y is

A.5x - 8y
B.9x + y
C.8x + 4y
D.6x + 5y

Answer: B

Add like terms.

\[ (5x + 3y) + (4x - 2y) = (5x + 4x) + (3y - 2y) \]

\[ = 9x + y \]

The \( y \) terms leave a coefficient of 1, which is written without the digit.

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134.

If a = 20, b = 35 and c = 5 then (4a + b) / c is

A.23
B.115
C.53
D.43

Answer: A

Substitute and work through the numerator first.

\[ 4a + b = 4(20) + 35 = 80 + 35 = 115 \]

\[ \frac{115}{c} = \frac{115}{5} = 23 \]

The whole numerator is divided by \( c \), not just the \( b \) - the 115 on offer is what you get by stopping one step early.

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135.

Factorization of p(4q + 3) +4(4q+3) leads to

A.(p - 4)(4q - 3)
B.4pq + 12q
C.(p + 4)(4q + 3)
D.4pq + 12 q

Answer: C

Both terms share the bracket \( (4q + 3) \).

\[ p(4q+3) + 4(4q+3) = (p + 4)(4q + 3) \]

Checking: \( 4pq + 3p + 16q + 12 \), which is what the original expands to.

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136.

Algebraic form of product of 7y and 4z is

A.11yz
B.3yz
C.11y + z
D.28yz

Answer: D

\[ 7y \times 4z = (7 \times 4)(y \times z) = 28yz \]

The coefficients multiply and the variables are written side by side. Adding them instead would give \( 11yz \) - the first option.

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137.

By factorizing \( 3x - 9y - 12z \), the answer will be

A.3(x - 3y + 4z)
B.3(x + 3y + 4z)
C.3(x + 3y - 4z)
D.3(x - 3y - 4z)

Answer: D

Each term is divisible by 3, so take it out.

\[ 3x - 9y - 12z = 3(x - 3y - 4z) \]

Both signs inside stay negative, since dividing \( -9y \) and \( -12z \) by \( +3 \) leaves them negative.

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138.

If a = 2, b = 4 and c =3 then 2ac[(2b + 3c)-c] is

A.11
B.51
C.168
D.12

Answer: C

Substitute \( a = 2 \), \( b = 4 \), \( c = 3 \) and work outward from the inner bracket.

\[ 2b + 3c = 8 + 9 = 17 \]

\[ 17 - c = 17 - 3 = 14 \]

\[ 2ac = 2 \times 2 \times 3 = 12 \]

\[ 12 \times 14 = 168 \]

The inner bracket must be evaluated before the multiplication by \( 2ac \).

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139.

In value 200x, variable is

A.10
B.200
C.x
D.10(20)

Answer: C

In \( 200x \), the number 200 is the coefficient - a fixed value - while \( x \) is the variable, the symbol that can take different values.

Anything expressed purely in numbers, such as \( 10(20) \), is a constant.

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140.

By solving expression 4[3s - 2(6s - 8)], answer will be

A.12s -16
B.16s - 12
C.\( -36s + 64 \)
D.16s + 12

Answer: C

Work from the inside out.

\[ 2(6s - 8) = 12s - 16 \]

\[ 3s - (12s - 16) = 3s - 12s + 16 = -9s + 16 \]

\[ 4(-9s + 16) = -36s + 64 \]

The minus in front of the inner bracket flips both its terms, turning \( -16 \) into \( +16 \).

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