If a = -12 and b = -14 then 2a + 2b + 3 is
Answer: B
Substitute \( a = -12 \) and \( b = -14 \).
\[ 2a = -24, \qquad 2b = -28 \]
\[ -24 - 28 + 3 = -49 \]
Both doubled values stay negative; the \( +3 \) only softens the total slightly.
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If algebraic expression 2w - [x -(y + z)] + 2w is solved then answer will be
Answer: C
Work outward from the innermost bracket.
\[ -(y + z) \text{ inside gives } x - y - z \]
\[ -[x - y - z] = -x + y + z \]
\[ 2w + (-x + y + z) + 2w = 4w - x + y + z \]
Two nested minus signs restore \( y \) and \( z \) to positive - the step the distractors are built around.
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If 6x + 2y - 4z is subtracted from 2x - 8y + 5z then answer will be
Answer: D
Subtracting flips every sign in the second expression.
\[ (2x - 8y + 5z) - (6x + 2y - 4z) \]
\[ = 2x - 8y + 5z - 6x - 2y + 4z \]
\[ = -4x - 10y + 9z \]
The \( -4z \) becomes \( +4z \), which is what makes the \( z \) coefficient \( +9 \).
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If x = 10 and y = 4 then 5x + 4y =
Answer: A
\[ 5x + 4y = 5(10) + 4(4) = 50 + 16 = 66 \]
Both products must be formed before adding; stopping at \( 5x \) gives 50.
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Sum of 2a + b + 5c and -5a - 2b + 3c is
Answer: C
Add the like terms.
\[ a: \ 2 - 5 = -3 \]
\[ b: \ 1 - 2 = -1 \]
\[ c: \ 5 + 3 = 8 \]
\[ \therefore\ -3a - b + 8c \]
The \( c \) terms are both positive, so that coefficient grows while the other two turn negative.
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On solving algebraic expression 2(x - 2y) +4(2y + 3z) -3(x + 4y - 5z), answer will be
Answer: B
Expand each bracket, then collect.
\[ 2(x - 2y) = 2x - 4y \]
\[ 4(2y + 3z) = 8y + 12z \]
\[ -3(x + 4y - 5z) = -3x - 12y + 15z \]
\[ x: \ 2 - 3 = -1; \quad y: \ -4 + 8 - 12 = -8; \quad z: \ 12 + 15 = 27 \]
\[ \therefore\ -x - 8y + 27z \]
The \( -3 \) turns \( -5z \) into \( +15z \), which is what makes the \( z \) coefficient large and positive.
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If algebraic expression is 2(x - y) + 3(4x -5y) then answer will be
Answer: A
Expand and collect.
\[ 2(x - y) = 2x - 2y \]
\[ 3(4x - 5y) = 12x - 15y \]
\[ (2x + 12x) + (-2y - 15y) = 14x - 17y \]
Both \( y \) terms are negative, so their coefficients add in magnitude.
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By factorizing following expression 5ab + 10ac + 15ad, answer must be
Answer: B
Every term shares the factor \( 5a \).
\[ 5ab + 10ac + 15ad = 5a(b + 2c + 3d) \]
Checking: \( 5a \times b = 5ab \), \( 5a \times 2c = 10ac \), \( 5a \times 3d = 15ad \). Taking out 5 alone would leave the \( a \) behind in each term.
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By factorizing algebraic expression cx + cy - dx - dy, answer will be
Answer: A
Group in pairs and factor each.
\[ cx + cy - dx - dy = c(x + y) - d(x + y) \]
\[ = (c - d)(x + y) \]
Taking out \( -d \) from the second pair turns \( -dx - dy \) into \( -d(x+y) \), matching the first bracket.
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Algebraic expression of word expression "2 times number a increased by 3" is
Answer: B
"2 times number \( a \)" is \( 2a \), and "increased by 3" adds 3 to it.
\[ 2a + 3 \]
The order matters: \( 3a + 2 \) would be three times the number increased by two.
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