Introduction: This is a short but important algebra topic. You must memorize the two expansion formulas. The questions are usually direct, but "A" level questions can involve simplification or using the formula to calculate values like 1023.

The "S Pass" Foundation (නියත S එකකට)

• Prompt 1 (Formula): Write the full expansion of (x+y)3.

• Prompt 2 (Formula): Write the full expansion of (x−y)3.

• Prompt 3 (Expand): Expand (p+3)3.

• Prompt 4 (Expand): Expand (m−1)3.

• Prompt 5 (Identify): Is x3+9x2+27x+27 the expansion of (x+3)3?

Climbing to a "C" (C එකට පාර)

• Prompt 1 (Expand): Expand (2a+b)3.

• Prompt 2 (Expand): Expand (x−3y)3.

• Prompt 3 (Calculate): Use the binomial expansion to find the value of 1013.

• Prompt 4 (Calculate): Use the binomial expansion to find the value of 993.

• Prompt 5 (Factorise): Write the expression 8a3−36a2b+54ab2−27b3 as the cube of a binomial.

Aiming for a "B" (B ඉලක්කය)

• Prompt 1 (Expand): Expand (3x+31​)3.

• Prompt 2 (Problem Solve): The side of a cube is (2x−1) cm. Find its volume and give the expanded expression.

• Prompt 3 (Find Coefficients): In the expansion of (x+p)3, the coefficient of the x2 term is 15. Find the value of p.

• Prompt 4 (Simplify): Simplify the expression (x+2)3−(x−2)3.

• Prompt 5 (Application): Verify that (x−3)3=x3−9x2+27x−27 by substituting x=5 into both sides of the equation.

Securing the "A" Distinction (A සාමාර්ථය තහවුරු කරගන්න)

• Prompt 1 (Challenge): If a+a1​=3, find the value of a3+a31​. (Hint: Cube the first equation).

• Prompt 2 (Challenge): If x−x1​=2, find the value of x3−x31​.

• Prompt 3 (Find Coefficients): In the expansion of (px+q)3, the coefficient of x3 is 64 and the constant term is -1. Find the possible values of p and q.

• Prompt 4 (Proof): Show that (a+b)3−(a3+b3)=3ab(a+b).

• Prompt 5 (Synthesis): Given that x2−4x+1=0, show that x3+x31​=52.