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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Expand and simplfy (x - y)(x + y)
Answer: C
\[ (x-y)(x+y) = x^{2} + xy - xy - y^{2} = x^{2} - y^{2} \]
The two middle terms cancel, which is exactly the difference-of-squares identity. The options with \( \pm 2xy \) are the expansions of \( (x \mp y)^{2} \).
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On evaluating algebraic expression -3(4s - 2t) - 4(2s + 3t), answer will be
Answer: A
Expand both brackets, distributing the negative signs.
\[ -3(4s - 2t) = -12s + 6t \]
\[ -4(2s + 3t) = -8s - 12t \]
\[ (-12s - 8s) + (6t - 12t) = -20s - 6t \]
The \( -3 \) turns \( -2t \) into \( +6t \), which is the sign most often lost.
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Factorise -20x² - 9x + 20
Answer: A
Test the candidate factorisation by expanding it.
\[ (5 + 4x)(4 - 5x) = 20 - 25x + 16x - 20x^{2} \]
\[ = -20x^{2} - 9x + 20 \]
which matches. The constant \( +20 \) needs both signs the same in the products \( 5 \times 4 \), and the \( -20x^{2} \) needs the two \( x \)-terms to have opposite signs - only this arrangement does both.
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pqr is what type of polynomial?
Answer: A
Polynomials are named by their number of terms, and terms are separated by \( + \) or \( - \).
\( pqr \) is a single product with no addition or subtraction, so it is one term - a monomial.
Three variables do not make three terms; \( p + q + r \) would be a trinomial.
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a²-b² is a product of
Answer: A
This is the difference of two squares.
\[ a^{2} - b^{2} = (a+b)(a-b) \]
Expanding checks it: \( a^{2} - ab + ab - b^{2} = a^{2} - b^{2} \), the middle terms cancelling. \( (a+b)^{2} \) and \( (a-b)^{2} \) both leave a \( \pm 2ab \) term behind.
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If a = 20, b = 35 and c = 5 then (4a + b) / c is
Answer: A
Substitute and work through the numerator first.
\[ 4a + b = 4(20) + 35 = 80 + 35 = 115 \]
\[ \frac{115}{c} = \frac{115}{5} = 23 \]
The whole numerator is divided by \( c \), not just the \( b \) - the 115 on offer is what you get by stopping one step early.
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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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If -4x + 5y is subtracted from 3x + 2y then answer will be
Answer: C
Subtracting means taking the first expression away from the second, so every sign in it flips.
\[ (3x + 2y) - (-4x + 5y) = 3x + 2y + 4x - 5y \]
\[ = 7x - 3y \]
The \( -4x \) becomes \( +4x \) under the subtraction - leaving it negative would give \( -x - 3y \).
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Which of the following is the value of (x+ 1/x)²?
Answer: C
Apply \( (p+q)^{2} = p^{2} + 2pq + q^{2} \) with \( p = x \) and \( q = \tfrac{1}{x} \).
\[ \left(x + \frac{1}{x}\right)^{2} = x^{2} + 2 \cdot x \cdot \frac{1}{x} + \frac{1}{x^{2}} \]
\[ = x^{2} + \frac{1}{x^{2}} + 2 \]
The middle term simplifies to the constant 2 because \( x \) cancels with \( \tfrac{1}{x} \) - which is why this identity is so useful for problems linking \( x + \tfrac{1}{x} \) to \( x^{2} + \tfrac{1}{x^{2}} \).
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