Question

(u^2+v^2-2uv) (u^2 + v^2 + 2uv) find the product of polynomials​

Answer 1

Answer: (u² + v² - 2uv)(u² + v² + 2uv) = u⁴ + v⁴ - 2u²v².

Explanation:

(u² + v² - 2uv)(u² + v² + 2uv)

= (u - v)²(u + v)²

{By indentities: a² + b² + 2ab = (a + b)², a² + b² - 2ab = (a - b)².}

= [(u + v)(u - v)]²

{aⁿbⁿ = (ab)ⁿ}

= [u² - v²]²

{As, (a + b)(a - b) = a² - b².}

= (u²)² + (v²)² - 2(u²)(v²)

= u⁴ + v⁴ - 2u²v².