If algebraic expression is [4(a + 2b - 3c) - 3(2b - 3c)] + 2a then answer will be
Answer: B
Expand each bracket, then collect.
\[ 4(a + 2b - 3c) = 4a + 8b - 12c \]
\[ -3(2b - 3c) = -6b + 9c \]
\[ (4a + 8b - 12c) + (-6b + 9c) + 2a = 6a + 2b - 3c \]
The \( -3 \) turns \( -3c \) into \( +9c \), which is what leaves only \( -3c \) at the end rather than \( -21c \).
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If \( a = 3 \), \( b = 2 \), \( c = 4 \) and \( x = 5 \), then the value of \( \dfrac{4ab - 2acx}{2ab + 3ac} \) is
Answer: A
Evaluate the numerator and denominator separately.
\[ 4ab = 4 \times 3 \times 2 = 24 \]
\[ 2acx = 2 \times 3 \times 4 \times 5 = 120 \]
\[ \text{numerator} = 24 - 120 = -96 \]
\[ 2ab = 12, \qquad 3ac = 36 \quad\Longrightarrow\quad \text{denominator} = 48 \]
\[ \frac{-96}{48} = -2 \]
Substituting into the whole numerator before dividing avoids the common error of cancelling term by term.
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By solving algebraic expression 2(3m -4n +5) -3(2m -3n +4), answer should be
Answer: B
Expand both brackets and collect.
\[ 2(3m - 4n + 5) = 6m - 8n + 10 \]
\[ -3(2m - 3n + 4) = -6m + 9n - 12 \]
\[ (6m - 6m) + (-8n + 9n) + (10 - 12) = n - 2 \]
The \( m \) terms cancel entirely, which is why no \( m \) appears in the answer.
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On evaluating expression 10(x - 20y) + 100x, answer will be
Answer: D
\[ 10(x - 20y) = 10x - 200y \]
\[ 10x - 200y + 100x = 110x - 200y \]
The 10 multiplies both terms inside the bracket, so the \( 20y \) becomes \( 200y \).
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If x = 5, y = 3 and z = 2 then xz (4y - 2z) is
Answer: B
Substitute \( x = 5 \), \( y = 3 \), \( z = 2 \) and clear the bracket first.
\[ 4y - 2z = 12 - 4 = 8 \]
\[ xz = 5 \times 2 = 10 \]
\[ 10 \times 8 = 80 \]
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On simplifying algebraic expression 2{4a + [-b -5(c + a -b)]}, answer will be
Answer: D
Work outward from the innermost bracket.
\[ -5(c + a - b) = -5c - 5a + 5b \]
\[ -b + (-5c - 5a + 5b) = -5a + 4b - 5c \]
\[ 4a + (-5a + 4b - 5c) = -a + 4b - 5c \]
\[ 2(-a + 4b - 5c) = -2a + 8b - 10c \]
The \( -5 \) flips the sign of \( -b \) inside, which is what turns the \( -b \) outside into a net \( +4b \).
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Algebraic form of statement "sum of product of 2a and 2b and product of 12x and 2y" is
Answer: A
Form each product, then add them.
\[ 2a \times 2b = 4ab \]
\[ 12x \times 2y = 24xy \]
\[ \therefore\ 4ab + 24xy \]
Both coefficients multiply within their own product; the two products are then joined by addition, not multiplied together.
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By factorization of (17x - 34), answer must be
Answer: C
Both terms share a factor of 17.
\[ 17x - 34 = 17x - 17 \times 2 = 17(x - 2) \]
Checking: \( 17x - 34 \). Taking out \( x \) instead is not possible, since 34 has no factor of \( x \).
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Algebraic expression of sum of 10a and 15c can be written as
Answer: A
"Sum" means addition, and the two terms are unlike - one in \( a \), the other in \( c \) - so they cannot be combined.
\[ 10a + 15c \]
Only like terms may be added; \( 25ac \) would be the result of a quite different operation.
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On simplifying expression 10x + 8x, answer will be
Answer: C
Both terms are in \( x \), so their coefficients add.
\[ 10x + 8x = (10 + 8)x = 18x \]
The variable itself is unchanged - writing 180x would multiply the coefficients instead of adding them.
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