If t = 50, u = 25 and v = 16 then (2t + 3u)(2u - v) + 2(t -u) is
Answer: D
Substitute \( t = 50 \), \( u = 25 \), \( v = 16 \) and evaluate each bracket first.
\[ 2t + 3u = 100 + 75 = 175 \]
\[ 2u - v = 50 - 16 = 34 \]
\[ 175 \times 34 = 5950 \]
\[ 2(t - u) = 2(50 - 25) = 50 \]
\[ 5950 + 50 = 6000 \]
The final addition is easy to overlook - 5950 is offered as the distractor for exactly that.
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Algebraic expression of word expression "subtract eight times of number b from ten times of number c" is
Answer: D
"Subtract eight times \( b \) from ten times \( c \)" means starting with \( 10c \) and taking \( 8b \) away.
\[ 10c - 8b \]
The phrase "subtract A from B" always puts B first - writing \( 8b - 10c \) reverses the two and gives the negative of the answer.
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By factorizing algebraic expression mp - np + mq - nq, answer will be
Answer: B
Group the terms in pairs and factor each.
\[ mp - np + mq - nq = p(m - n) + q(m - n) \]
\[ = (p + q)(m - n) \]
The bracket \( (m-n) \) appears in both parts, so it comes out as the common factor.
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If the expression \( 4c + 4b + 4d \) is subtracted from \( 3c + 4b + 5d \), then the answer will be
Answer: A
Subtracting flips every sign in the expression being taken away.
\[ (3c + 4b + 5d) - (4c + 4b + 4d) \]
\[ = (3c - 4c) + (4b - 4b) + (5d - 4d) \]
\[ = -c + d \]
The \( b \) terms cancel exactly, which is why no \( b \) survives.
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By factorizing 54x - 45y, answer must be
Answer: A
Both terms share a factor of 9.
\[ 54x - 45y = 9 \times 6x - 9 \times 5y = 9(6x - 5y) \]
9 is the highest common factor of 54 and 45; taking out 3 alone would leave \( 3(18x - 15y) \), which is not fully factorised.
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By factorizing algebraic expression 36ab - 48bc, answer must be
Answer: C
Look for the common factors of the coefficients and the variables.
\[ 36ab - 48bc = 6b(6a - 8c) \]
Checking: \( 6b \times 6a = 36ab \) and \( 6b \times 8c = 48bc \).
The variable \( b \) appears in both terms and comes out; \( a \) and \( c \) do not. A fuller factorisation is \( 12b(3a - 4c) \), but among the options only \( 6b(6a - 8c) \) expands back correctly.
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Sum of 2a + 4b, 5a + 2c + 2d, -5a - 9b + 4c - d and 11b - 8c - 4d is
Answer: B
Collect each variable in turn.
\[ a: \ 2 + 5 - 5 = 2 \]
\[ b: \ 4 - 9 + 11 = 6 \]
\[ c: \ 2 + 4 - 8 = -2 \]
\[ d: \ 2 - 1 - 4 = -3 \]
\[ \therefore\ 2a + 6b - 2c - 3d \]
Taking one variable at a time across all four expressions is safer than adding them two at a time.
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In 15y and 160ab, coefficients are
Answer: D
The coefficient is the numerical factor of a term.
\[ 15y \rightarrow 15, \qquad 160ab \rightarrow 160 \]
The letters \( y \), \( a \) and \( b \) are the variable parts, not coefficients.
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Answer of factorization of expression 8a(2x + 4y) - (2x + 4y) is
Answer: A
Both terms share the bracket \( (2x + 4y) \), the second with an unwritten coefficient of 1.
\[ 8a(2x+4y) - 1 \cdot (2x+4y) = (8a - 1)(2x + 4y) \]
That invisible 1 becomes the \( -1 \) in the first bracket; dropping it would lose a whole term.
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Statement 7a divided by 8b can be expressed algebraically as
Answer: C
"7a divided by 8b" is written as a fraction with the first quantity on top.
\[ \frac{7a}{8b} \]
Reversing it gives \( \tfrac{8b}{7a} \), the reciprocal, and multiplying instead of dividing gives \( 56ab \).
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