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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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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Simplify a(c - b) - b(a - c)
Answer: B
Expand both brackets, watching the sign in front of the second.
\[ a(c-b) - b(a-c) = ac - ab - ab + bc \]
\[ = ac - 2ab + bc \]
The minus outside the second bracket flips both of its terms, which is what turns \( -bc \) into \( +bc \) and produces the \( -2ab \).
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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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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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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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Factorise x² + x - 72
Answer: C
Find two numbers whose product is \( -72 \) and whose sum is \( +1 \).
\[ 9 \times (-8) = -72, \qquad 9 + (-8) = 1 \]
\[ x^{2} + x - 72 = (x - 8)(x + 9) \]
Checking: \( x^{2} + 9x - 8x - 72 = x^{2} + x - 72 \). Swapping the signs would give a middle term of \( -x \).
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Coefficient of x² in 4x³ + 3x² - x + 1 is:
Answer: C
Read off the number multiplying \( x^{2} \) in
\[ 4x^{3} + 3x^{2} - x + 1 \]
The coefficient is 3. The \( -1 \) belongs to \( x \) and the \( 4 \) to \( x^{3} \).
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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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By factorizing \( 3x - 9y - 12z \), the answer will be
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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