Question

Разложить на множители:16x^4y^2+12x^2y^4-20x^8y^2-15x^6y^4

Answer 1

16x⁴y²+12x²y⁴-20x⁸y²-15x⁶y⁴=(16x⁴y²+12x²y⁴)-(20x⁸y²+15x⁶y⁴)=
4х²у²(4х²+3у²)-5х⁶у²(4х²+3у²)=(4х²+3у²)(4х²у²-5х⁶у²)=х²у²(4х²+3у²)(4-5х⁴)

Answer 2

$\16x^4y^2+12x^2y^4-20x^8y^2-15x^6y^4= \ \4x^2y^2(4x^2+3y^2)-5x^6y^2(4x^2+3y^2)=(4x^2+3y^2)(4x^2y^2-5x^6y^2)= \ \x^2y^2(4-5x^4)(4x^2+3y^2)=x^2y^2(2-x^2sqrt5)(2+x^2sqrt5)(4x^2+3y^2)= \ \x^2y^2(sqrt2-xsqrt[4]5)(sqrt2+xsqrt[4]5)(2+x^2sqrt5)(4x^2+3y^2)$