Question

Factorize the given expression: 9x^2 + 49y^2 + 25z^2 - 42xy - 30xz + 70yz

Answer 1

Answer:

9x2 + 49y2 + 25z2 - 42xy - 30xz + 70yz

= (-3x)2 + (7y)2 + (5z)2 + 2(-3x)(7y) + 2(-3x)(5z) + 2(7y)(5z)

(-3x)2 + (7y)2 + (5z)2 + 2(-3x)(7y) + 2(-3x)(5z) + 2(7y)(5z) resembles a2 + b2 + c2 + 2ab + 2bc + 2ca

∴ (-3x)2 + (7y)2 + (5z)2 + 2(-3x)(7y) + 2(-3x)(5z) + 2(7y)(5z) = (-3x + 7y + 5z)2

= (-3x + 7y + 5z)(-3x + 7y + 5z)