## Pages

### Solved Example 1

Expand the expression (x + 2y)^3

### Solution

Compare the given expression with (a + b)^3. Thus,
a = x and b = 2y
Write the formula,
(a + b)^3 = a^3 + b^3 + 3ab(a + b)
Put 'x' in place of 'a' and '2y' in place of 'b',
(x + 2y)^3 = x^3 + (2y)^3 + 3(x)(2y)(x + 2y)
Simplify the expression,
(x + 2y)^3 = x^3 + 8y^3 + 6x^2y + 12xy^2

### Solved Example 2

Expand the expression (3a + 4b)^3

### Solution

Compare the given expression with (a + b)^3. Thus,
a = 3a and b = 4b
Write the formula,
(a + b)^3 = a^3 + b^3 + 3ab(a + b)
Put '3a' in place of 'a' and '4b' in place of 'b',
(3a + 4b)^3 = (3a)^3 + (4b)^3 + 3(3a)(4b)(3a + 4b)
Simplify the expression,
(3a + 4b)^3 = 27a^3 + 64b^3 + 36ab(3a + 4b)
= 27a^3 + 64b^3 + 108a^2b + 144ab^2

### Solved Example 3

Expand the expression (x + y/2)^3

### Solution

Compare the given expression with (a + b)^3. Thus,
a = x and b = y/2
Write the formula,
(a + b)^3 = a^3 + b^3 + 3ab(a + b)
Put x in place of 'a' and y/2 in place of 'b',
(x + y/2)^3 = (x)^3 + (y/2)^3 + 3(x)(y/2)(x + y/2)
Simplify the expression,
(x + y/2)^3 = x^3 + (y^3)/8 + (3xy)/2(x + y/2)
= x^3 + (y^3)/8 + (3x^2y)/2 + (3xy^2)/4

### Solved Example 4

Expand the expression (x/3 + y/4)^3

### Solution

Compare the given expression with (a + b)^3. Thus,
a = x/3 and b = y/4
Write the formula,
(a + b)^3 = a^3 + b^3 + 3ab(a + b)
Put x/3 in place of 'a' and y/4 in place of 'b',
(x + y/2)^3 = (x)^3 + (y/2)^3 + 3(x)(y/2)(x + y/2)
Simplify the expression,
(x + y/2)^3 = x^3 + (y^3)/8 + (3xy)/2(x + y/2)
= x^3 + (y^3)/8 + (3x^2y)/2 + (3xy^2)/4