A) x² -3x+xy-3y=x²+xy-3x-3y=x(x+y)-3(x+y)=(x+y)(x-3)

\(x^2-3x+xy-3y\)

\(=\left(x^2+xy\right)-\left(3x+3y\right)\)

\(=x.\left(x+y\right)-3.\left(x+y\right)\)

\(=\left(x-3\right).\left(x+y\right)\)

\(2x^2-x+2xy-y\)

\(=2x^2-\left(x-2xy+y\right)\)

\(=2x^2-\left(x-y\right)^2\)

\(=\left(\sqrt{2}x\right)^2-\left(x-y\right)^2\)

\(=\left(\sqrt{2}x-x+y\right).\left(\sqrt{2}x+x-y\right)\)

\(x^4+x^3+2x^2+x+1\)

\(=\left(x^4+2x^2+1\right)+\left(x^3+x\right)\)

\(=\left(x^2+1\right)^2+x.\left(x^2+1\right)\)

\(=\left(x^2+1\right).\left(x^2+1+x\right)\)

\(16+2xy-x^2-y^2\)

\(=16-x^2+2xy-y^2\)

\(=16-\left(x^2-2xy+y^2\right)\)

\(=4^2-\left(x-y\right)^2\)

\(=[4-\left(x-y\right)].[4+\left(x-y\right)]\)

\(=\left(4-x+y\right).\left(4+x-y\right)\)

\(\left(2x+1\right)^2-2.\left(x-3\right).\left(2x+2\right)+\left(x-3\right)^2\)

\(=\left(2x+1\right)^2-2.\left(2x+1\right).\left(3-x\right)+\left(3-x\right)^2\)

\(=[\left(2x+1\right)-\left(3-x\right)]^2\)

\(=\left(2x+1-3x+x\right)^2\)

\(=\left(3x-2\right)^2\)

\(5.\left(2x-3\right)+6x=10x-15+6x=16x-15\)

\(\left(x+5\right).\left(x+1\right)-x^2=x^2+x+5x+5-x^2=6x+5\)

\(\left(x-3\right).\left(x+3\right)+\left(2-x\right)^2=x^2-9+4-4x+x^2=2x^2-4x-5\)

\(\left(x-2\right).\left(x+1\right)-x^2+3=x^2+x-2x-2-x^2+3=-x+1\)

\(\left(x+2\right)^2-3x.\left(x+1\right)=x^2+4x+4-3x^2-3x=-2x^2+x+4\)

\(\left(x+4\right).\left(x^2-4x+16\right)=x^3+4^3=x^3+64\)

\(\left(3x-2\right).\left(9x^2+6x+4\right)=\left(3x\right)^3-2^3=27x^3-8\)

a=130 và d=50

=>a+d=180

mà a và d là hai góc tcp

=>ab//cd

=>là hình thang

mà hai đg chéo ac=bd

=>HBH

Gửi bạn nè. Chúc bạn học tốt !

\(4x^2-25+\left(2x+7\right).\left(5-2x\right)\)

\(=\left(2x+5\right).\left(2x-5\right)-\left(2x+7\right).\left(2x-5\right)\)

\(=\left(2x+5-2x-7\right).\left(2x-5\right)\)

\(=-2.\left(2x-5\right)\)

\(a^2x^2-a^2x^2-b^2x^2+b^2y^2\)

\(=a^2.\left(x^2-y^2\right)-b^2.\left(x^2-y^2\right)\)

\(=\left(a^2-b^2\right).\left(x^2-y^2\right)\)

\(=\left(a-b\right).\left(a+b\right).\left(x-y\right).\left(x+y\right)\)

\(x^2-y^2+12y-36\)

\(=x^2-\left(y^2-12y+36\right)\)

\(=x^2-\left(y-6\right)^2\)

\(=\left(x-y+6\right).\left(x+y-6\right)\)

\(\left(x+2\right)^2-x^2+2x-1\)

\(=\left(x+2\right)^2-\left(x^2-2x+1\right)\)

\(=\left(x+2\right)^2-\left(x-1\right)^2\)

\(=[x+2-\left(x-1\right)].[x+2+\left(x-1\right)]\)

\(=\left(x+2-x+1\right).\left(x+2+x-1\right)\)

\(=3.\left(2x+1\right)\)

\(16x^2-y^2=\left(4x\right)^2-y^2=\left(4x-y\right).\left(4x+y\right)\)

\(1+27x^3=1^3+\left(3x\right)^3=\left(1+3x\right).\left(1-3x+9x^2\right)\)

\(4x^2-4x-3\)

\(=4x^2-2x+6x-3\)

\(=2x.\left(x-1\right)+3.\left(x-1\right)\)

\(=\left(2x+3\right).\left(x-1\right)\)

\(x^2-4x+3\)

\(=x^2-3x-x+3\)

\(=\left(x^2-x\right)-\left(3x-3\right)\)

\(=x.\left(x-1\right)-3.\left(x-1\right)\)

\(=\left(x-3\right).\left(x-1\right)\)

\(x^4-8x+63\)

\(=x^4+4x^3+9x^2-4x^3-16x^2-36x+7x^2+28x+63\)

\(=\left(x^4+4x^3+9x^2\right)-\left(4x^3+16x^2+36x\right)+\left(7x^2+28x+63\right)\)

\(=x^2.\left(x^2+4x+9\right)-4x.\left(x^2+4x+9\right)+7.\left(x^2+4x+9\right)\)

\(=\left(x^2-4x+7\right).\left(x^2+4x+9\right)\)

\(\left(4x^4+4x^3-16x^2-16x\right):\left(4x+4\right)\)

\(=[\left(4x^4+4x^3\right)-\left(16x^2+16x\right)]:\left(4x+4\right)\)

\(=[4x^3.\left(x+1\right)-16x.\left(x+1\right)]:\left(4x+4\right)\)

\(=[\left(4x^3-16x\right).\left(x+1\right)]:\left(4x+4\right)\)

\(=[4.\left(x^3-4x\right).\left(x+1\right)]:[4.\left(x+1\right)]\)

\(=\frac{4.\left(x+1\right).\left(x^3-4x\right)}{4.\left(x+1\right)}\)

\(=x^3-4x\)