Question

expand each expression using algebraic identities
1. (a-bc)^2
2. (1+2n)^2​

Answer 1

Formula used -

(a - b)² = a² - 2ab + b²

(a + b)² = a² + 2ab + b²

1.

(a - bc)²

= (a)² - 2(a)(bc) + (bc)²

[by the formula (a - b)² = a² - 2ab + b², here a = a, and b = bc]

= (a)² - 2(a)(bc) + (bc)²

= a² - 2abc + (bc)²

Hence (a - bc)² = a² - 2abc + (bc)²

2.

(1 + 2n)²

= (1)² + 2(1)(2n) + (2n)²

[by the formula (a + b)² = a² + 2ab + b², here a = 1 and b = 2n]

= (1)² + (2×1×2n) + (2n)²

= 1 + 4n + 4n²

Hence (1 + 2n)² = 1 + 4n + 4n²

hope it helps.