Online Test — Expansions
10 Questions • 15 min • Chapter MCQ
15:00
Question 1 of 10
medium
What is the expanded form of the algebraic binomial (2a - 3b)²?
4a² - 9b²
4a² - 12ab + 9b²
4a² + 12ab + 9b²
4a² - 6ab + 9b²
Explanation: Use (x - y)² = x² - 2xy + y². The middle term is -2(2a)(3b) = -12ab.
Question 2 of 10
medium
Find the value of the middle linear coefficient when expanding (x + 7)(x - 4).
11
-3
3
-28
Explanation: The middle term coefficient is the sum of the constants: 7 + (-4) = 3.
Question 3 of 10
medium
Evaluate the numerical calculation 51 × 49 using an identity shortcut.
2,499
2,501
2,500
2,400
Explanation: Use difference of squares: (50 + 1)(50 - 1) = 2500 - 1 = 2499.
Question 4 of 10
medium
If x + (1/x) = 4, find the numerical value of x² + (1/x²).
16
18
14
12
Explanation: Square both sides: (x + 1/x)² = 16 -> x² + 2 + 1/x² = 16 -> Subtract 2 to get 14.
Question 5 of 10
medium
How many individual terms are there in the unsimplified expansion of (x + y + z)²?
3
4
6
9
Explanation: The trinomial square expansion contains 3 squared terms and 3 paired terms, totaling 6.
Question 6 of 10
medium
If a + b + c = 0, then the value of the cubic sum a³ + b³ + c³ is identical to:
0
a² + b² + c²
3abc
-3abc
Explanation: This is the standard conditional identity definition for a zero sum.
Question 7 of 10
medium
What is the expanded form of (a + b)³?
a³ + b³
a³ + b³ + 3a²b + 3ab²
a³ - b³ + 3ab
a³ + b³ + 2ab
Explanation: This is the standard long-form cubic expansion for a sum.
Question 8 of 10
medium
Expand and simplify the expression (x + 2y)(x - 2y).
x² - 2y²
x² - 4y²
x² + 4y²
x² - 4xy + 4y²
Explanation: Applying the difference of two squares identity: x² - (2y)² = x² - 4y².
Question 9 of 10
medium
If a² + b² + c² = 20 and ab + bc + ca = 8, calculate the value of (a + b + c)².
28
36
16
40
Explanation: Formula: (a+b+c)² = (a²+b²+c²) + 2(ab+bc+ca) = 20 + 2(8) = 20 + 16 = 36.
Question 10 of 10
medium
Find the value of (15)³ + (-10)³ + (-5)³ using conditional rules.
0
750
2,250
1,500
Explanation: The sum 15-10-5=0. Value = 3abc = 3 × 15 × (-10) × (-5) = 2250.