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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Algebraic form of statement "sum of product of 2a and 2b and product of 12x and 2y" is
Answer: A
Form each product, then add them.
\[ 2a \times 2b = 4ab \]
\[ 12x \times 2y = 24xy \]
\[ \therefore\ 4ab + 24xy \]
Both coefficients multiply within their own product; the two products are then joined by addition, not multiplied together.
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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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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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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 a = 2, b = 4 and c =3 then 2ac[(2b + 3c)-c] is
Answer: C
Substitute \( a = 2 \), \( b = 4 \), \( c = 3 \) and work outward from the inner bracket.
\[ 2b + 3c = 8 + 9 = 17 \]
\[ 17 - c = 17 - 3 = 14 \]
\[ 2ac = 2 \times 2 \times 3 = 12 \]
\[ 12 \times 14 = 168 \]
The inner bracket must be evaluated before the multiplication by \( 2ac \).
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If t = 50, u = 25 and v = 16 then (2t + 3u)(2u - v) + 2(t -u) is
Answer: D
Substitute \( t = 50 \), \( u = 25 \), \( v = 16 \) and evaluate each bracket first.
\[ 2t + 3u = 100 + 75 = 175 \]
\[ 2u - v = 50 - 16 = 34 \]
\[ 175 \times 34 = 5950 \]
\[ 2(t - u) = 2(50 - 25) = 50 \]
\[ 5950 + 50 = 6000 \]
The final addition is easy to overlook - 5950 is offered as the distractor for exactly that.
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Statement 7a divided by 8b can be expressed algebraically as
Answer: C
"7a divided by 8b" is written as a fraction with the first quantity on top.
\[ \frac{7a}{8b} \]
Reversing it gives \( \tfrac{8b}{7a} \), the reciprocal, and multiplying instead of dividing gives \( 56ab \).
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What is the product of (x+a) and (x+b)?
Answer: D
Expand term by term.
\[ (x+a)(x+b) = x^{2} + bx + ax + ab \]
\[ = x^{2} + (a+b)x + ab \]
The coefficient of \( x \) is the sum of the two constants and the last term their product - the standard pattern used when factorising quadratics.
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If x = 5, y = 3 and z = 2 then xz (4y - 2z) is
Answer: B
Substitute \( x = 5 \), \( y = 3 \), \( z = 2 \) and clear the bracket first.
\[ 4y - 2z = 12 - 4 = 8 \]
\[ xz = 5 \times 2 = 10 \]
\[ 10 \times 8 = 80 \]
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