If x = +7 and y = -8 then x + 3y is
Answer: C
Substitute \( x = 7 \) and \( y = -8 \), multiplying before adding.
\[ x + 3y = 7 + 3(-8) = 7 - 24 = -17 \]
The 3 multiplies \( y \) only, so it is \( -24 \) that is added, not \( -8 \) - that slip would give \( -1 \).
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By factorizing algebraic expression bc + bd + yc + yd, answer will be
Answer: C
Group in pairs and factor each.
\[ bc + bd + yc + yd = b(c + d) + y(c + d) \]
\[ = (b + y)(c + d) \]
Both signs are positive throughout, so the answer carries no minus.
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On simplifying expression 13y + 2z + 3y, answer will be
Answer: B
Only the \( y \) terms are alike.
\[ 13y + 3y = 16y \]
\[ \therefore\ 16y + 2z \]
The \( z \) term is unlike and stays as it is; it cannot be merged with the \( y \) terms.
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By factorizing algebraic expression 4px - 8qx - 3py + 6qy, answer will be
Answer: D
Group in pairs and factor each.
\[ 4px - 8qx - 3py + 6qy = 4x(p - 2q) - 3y(p - 2q) \]
\[ = (4x - 3y)(p - 2q) \]
Taking out \( -3y \) rather than \( 3y \) from the second pair is what makes both brackets read \( (p - 2q) \).
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Algebraic expression of word expression "product of 8 and four times of a number c" is
Answer: C
Four times the number is \( 4c \), and the product of 8 with that is
\[ 8 \times 4c = 32c \]
The two multiplications compound; adding them instead would give \( 8 + 4c \).
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Sum of 2s + 4t -3u + 5v, -s + 2t + 9u - 11v and 3s - 4t + 2u - 3v is
Answer: D
Collect each variable across the three expressions.
\[ s: \ 2 - 1 + 3 = 4 \]
\[ t: \ 4 + 2 - 4 = 2 \]
\[ u: \ -3 + 9 + 2 = 8 \]
\[ v: \ 5 - 11 - 3 = -9 \]
\[ \therefore\ 4s + 2t + 8u - 9v \]
The options differ only in the signs of the \( t \) and \( u \) terms, so those two columns decide the answer.
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By simplifying expression 8(5x + 2y), answer is
Answer: D
The 8 multiplies both terms inside the bracket.
\[ 8(5x + 2y) = 40x + 16y \]
Multiplying only the first term would give \( 40x + 2y \); the distributive law applies to every term.
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On solving expression 6a + 8b - 11a, answer will be
Answer: A
Only the \( a \) terms are alike.
\[ 6a - 11a = -5a \]
\[ \therefore\ -5a + 8b \]
Since \( 11 > 6 \), the result is negative; the \( 8b \) is unlike and stays put.
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Algebraic expression of difference of 13x and 7y can be written as
Answer: B
"Difference of 13x and 7y" means the first minus the second.
\[ 13x - 7y \]
The two terms are unlike, so the subtraction cannot be carried out any further - \( 6xy \) would come from subtracting the coefficients and merging the variables, which is not a valid step.
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If a = -5, b = 2 and c = 3 then 2a - 4ab + 3bc is
Answer: D
Substitute \( a = -5 \), \( b = 2 \), \( c = 3 \), taking each product separately.
\[ 2a = -10 \]
\[ -4ab = -4(-5)(2) = +40 \]
\[ 3bc = 3(2)(3) = 18 \]
\[ -10 + 40 + 18 = 48 \]
The middle term turns positive because two negatives multiply - treating it as \( -40 \) gives \( -32 \).
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