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\(a,2x^3y-2xy=2xy\left(x^2-1\right)=2xy\left(x-1\right)\left(x+1\right)\)
\(b,x^2-2x-4x^2-4x=-3x^2-2x-4x\\ =-3x^2-6x=-3\left(x^2+2x\right)=-3x\left(x+2\right)\)
\(2x^2-5xy-3y^2\)
=\(2x^2+xy-6xy-3y^2\)
\(=x\left(2x+y\right)-3y\left(2x+y\right)\)
=\(\left(x-3y\right)\left(2x+y\right)\)
Ta có :
2x^2-5xy-3y^2
= 2^x + xy - 6xy - 3y^2
= x(2x + y) - 3y(2x + y)
= (2x + y)(x - 3y)
(12x^2 - 12xy + 3y^2) - 10.(2x - y) + 8
= 3(4x^2 - 4xy + y^2) - 10(2x - y) + 8
= 3(2x - y)^2 - 10(2x - y) + 8
= 3(2x - y)^2 - 10(2x - y) + 8
= 3(2x - y)^2 - 6(2x - y) - 4(2x - y) + 8
= 3(2x - y)(2x - y - 2) - 4(2x - y -2)
= (2x - y -2)[3(2x - y) - 4]
= (2x - y -2)(6x - 3y -4)
Ai k mk mk k lại
(12x^2 - 12xy + 3y^2) - 10.(2x - y) + 8
= 3(4x^2 - 4xy + y^2) - 10(2x - y) + 8
= 3(2x - y)^2 - 10(2x - y) + 8
= 3(2x - y)^2 - 10(2x - y) + 8
= 3(2x - y)^2 - 6(2x - y) - 4(2x - y) + 8
= 3(2x - y)(2x - y - 2) - 4(2x - y -2)
= (2x - y -2)[3(2x - y) - 4]
= (2x - y -2)(6x - 3y -4)
2x^2-5xy-3y^2
= 2^x + xy - 6xy - 3y^2
= x(2x + y) - 3y(2x + y)
= (2x + y)(x - 3y)
\(9\left(x-3y\right)^2-25\left(2x+y\right)^2\)
\(=\left[3\left(x-3y\right)\right]^2-\left[5\left(2x+y\right)\right]^2\)
\(=\left(3x-9y\right)^2-\left(10x+5y\right)^2\)
\(=\left[3x-9y+10x+5y\right]\left[3x-9y-\left(10x+5y\right)\right]\)
\(=\left(13x-4y\right)\left(-7x-14y\right)\)
\(=-7\left(x+2y\right)\left(13x-4y\right)\)
9(x - 3y)² - 25(2x + y)²
= 3².(x - 3y)² - 5².(2x + y)²
= (3x - 9y)² - (10x + 5y)²
= (3x - 9y - 10x - 5y)(3x - 9y + 10x + 5y)
= (-7x - 14y)(13x - 4y)
= -7(x + 2y)(13x - 4y)
\(a,-2x^3y^4-4x^4y^3+2x^3y^3\)
\(=-2x^3y^3\left(y+x-1\right)\)
\(b,ab\left(x-5\right)-a^2\left(5-x\right)\)
\(=\left(x-5\right)\left(ab+a^2\right)\)
Ta có: \(\left(2x+3y\right)^2-2\left(2x+3y\right)\)
\(=\left(2x+3y\right)\left(2x+3y-2\right)\)
\(\left(2x+3y\right)^2-2\left(2x+3y\right)=\left(2x+3y-2\right)\left(2x+3y\right)\)