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Find H.C.F. from 4x^4 + 19x^(2)y^(2) + 49y^4 and 4x^3 + 14xy^2 - 6x^(2)y

I did the 2nd exprn, but I'm stuck in 1st. pls help.

1st expression:
= 4x^4 + 19x^(2)y^(2) + 49y^4

2nd expression:
= 4x3 + 14xy2 - 6x2y
= 2x(2x2 + 7y2 - 3xy)
= 2x(2x2 - 3xy + 7y2)

rames asked a year ago·

Here is the solution.

1st expression:
= 4x^4 + 19x^(2)y^(2) + 49y^4
= (2x2)2 + (7y2)2 + 19x2y2
= (2x2 + 7y2)2 - 28x2y2 + 18x2y2
= (2x2 + 7y2)2 - 9x2y2
= (2x2 + 7y2 + 3xy)(2x2 + 7y2 - 3xy)
= (2x2 + 3xy + 7y2)(2x2 - 3xy + 7y2)

2nd expression:
= 4x3 + 14xy2 - 6x2y
= 2x(2x2 + 7y2 - 3xy)
= 2x(2x2 - 3xy + 7y2)

Video explanation:

dibas answered a year ago