Question

9. Expand
(i) (x + 5y + 6z)^2
(ii) (2a -3b + 4c)^2
(iii) (-a + 2b)^3

Answer 1

`(i) \(x^2 + 10xy + 12xz + 25y^2 + 60yz + 36z^2\)(ii) \(4a^2 - 24ab + 16ac - 9b^2 + 24bc + 16c^2\)(iii) \(-a^3 - 6a^2b - 12ab^2 - 8b^3\)`

Explanation:

Sure, I can help you simplify the expanded expressions. Let's work through each one:

(i)
`\((x + 5y + 6z)^2\)`

Expanding using the formula
`\((a + b)^2 = a^2 + 2ab + b^2\):`

`\((x + 5y + 6z)^2 = x^2 + 2x(5y + 6z) + (5y + 6z)^2\)\[x^2 + 10xy + 12xz + 25y^2 + 60yz + 36z^2\]`

(ii)
`\((2a - 3b + 4c)^2\)`

Expanding using the formula
`\((a + b)^2 = a^2 + 2ab + b^2\):`

`\((2a - 3b + 4c)^2 = (2a)^2 + 2(2a)(-3b + 4c) + (-3b + 4c)^2\)`

Simplify:

`\[4a^2 - 12ab + 16ac - 12ab + 24bc - 9b^2 + 16c^2\]`

Combine like terms:

`\[4a^2 - 24ab + 16ac - 9b^2 + 24bc + 16c^2\]`

(iii)
`\((-a + 2b)^3\)`

Expanding using the formula
`\((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\):`

`\((-a + 2b)^3 = (-a)^3 + 3(-a)^2(2b) + 3(-a)(2b)^2 + (2b)^3\)`

Simplify:

`\[-a^3 - 6a^2b - 12ab^2 - 8b^3\]`