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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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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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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Answer of factorization of expression (3x - 2y)(a + b) + (4x - 3y)(a + b) is
Answer: D
Both terms share the factor \( (a + b) \), so take it out first:
\[ (3x - 2y)(a+b) + (4x - 3y)(a+b) = \left[(3x - 2y) + (4x - 3y)\right](a+b) \]
Collecting like terms inside the bracket:
\[ 3x + 4x = 7x, \qquad -2y - 3y = -5y \]
\[ \therefore\; (7x - 5y)(a + b) \]
The sign is the trap: both \( y \) terms are negative, so they add to \( -5y \) rather than cancelling.
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Expand and simplfy (x - 5)(x + 4)
Answer: D
\[ (x-5)(x+4) = x^{2} + 4x - 5x - 20 \]
\[ = x^{2} - x - 20 \]
The constants \( -5 \) and \( +4 \) sum to \( -1 \) for the middle term and multiply to \( -20 \) for the last.
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