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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What degree does x³ - x²y² - 8y²+ 2 have?
Answer: C
The degree of a polynomial is the highest total degree among its terms.
The largest is 4. In a term with several variables the exponents are added, which is what puts \( x^{2}y^{2} \) above \( x^{3} \).
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On simplifying expression 10x + 8x, answer will be
Answer: C
Both terms are in \( x \), so their coefficients add.
\[ 10x + 8x = (10 + 8)x = 18x \]
The variable itself is unchanged - writing 180x would multiply the coefficients instead of adding them.
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By simplifying expression 8(5x + 2y), answer is
Answer: D
The 8 multiplies both terms inside the bracket.
\[ 8(5x + 2y) = 40x + 16y \]
Multiplying only the first term would give \( 40x + 2y \); the distributive law applies to every term.
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