Question

Factories using identities: 16x²-40xy+25y²

Answer 1

Explanation:

$\mathsf{16x^2-40xy+25y^2}$

$\mathsf{=(4x)^2-2(4x)(5y)+(5y)^2}$

$\mathsf{=(4x-5y)^2}$ [∵ $\mathsf{a^2-2ab+b^2=(a-b)^2}$, proof below]

$\mathsf{=(4x-5y)(4x-5y)}$

Verification of identity:

$\mathsf{(a-b)^2=(a-b)(a-b)}$

$\mathsf{=(a-b)a+(a-b)(-b)}$

$\mathsf{=a^2-ab-ab+b^2}$

$\mathsf{=a^2-2ab+b^2}$

Answer: (4x-5y)(4x-5y)

I hope this helps. :D