Разложите на множители:
а) 18a^2-2
б) 2ax^3-16ay^3
в) 4a^4y-8a^2by+4b^2y
г) 9m^2-6m-10p-25p^2
д) 9x^2+9ax^2-y^2+ay^2+6axy
а) 18a^2-2
б) 2ax^3-16ay^3
в) 4a^4y-8a^2by+4b^2y
г) 9m^2-6m-10p-25p^2
д) 9x^2+9ax^2-y^2+ay^2+6axy
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Answers & Comments
б) 2ax^3-16ay^3=2a(x³-8y³)=2a(x-2y)(x²+2xy+4y²)
в) 4a^4y-8a^2by+4b^2y=4(a⁴y-2a²by+b²y)=
4(a⁴y-a²by-a²by+b²y)=4((a⁴y-a²by)+(b²y-a²by))=
4((a²y(a²-b)+by(b-a²))=4((a²y(a²-b)-by(a²-b))=
4(a²-b)(a²y-by)=4y(a²-b)(a²-b)=4y(a²-b)²
г) 9m^2-6m-10p-25p^2=(9m²-25p²)-(6m+10p)=
(3m-5p)(3m+5p)-2(3m+5p)=(3m+5p)(3m-5p-2)
д) 9x^2+9ax^2-y^2+ay^2+6axy=
(9x²-y²)+(9ax²+6axy+ay²)=(3x-y)(3x+y)+a(9x²+6xy+y²)=(3x-y)(3x+y)+a(3x+y)²=
(3x+y)(3x-y+a(3x+y))=(3x+y)(3x-y+3ax+ay)