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giải hộ câu c, d và f thôi nhá, mấy câu kia biết là rồi
3x^2(5x^2-7x+4)
=15x^4-21x^3+12x^2
xy^2(2x^2y-5xy+y)
=2x^3y^3-5x^2y^3+xy^3
(2x^2-5x)(3x^2-2x+1)
=6x^4-4x^3+2x^2-15x^3+10x^2-5x
=6x^4-19x^3+12x^2-5x
(x-3y)(2xy+y^2+x)
=2x^2y+xy^2+x^2-6xy^2-3y^3-3xy
=-3y^3+2x^2y-5xy^2+x^2-3xy
\(P=\left(x-y\right)^2+\left(x+y\right)^2-2\left(x+y\right)\left(x-y\right)-4x^2=\left(x-y-x-y\right)^2-\left(2x\right)^2=\left(-2y\right)^2-\left(2x\right)^2\)
\(=\left(2y-2x\right)\left(2y+2x\right)=2\left(y-x\right)2\left(y+x\right)=4\left(x+y\right)\left(y-x\right)\)
\(x^3-x^2y+3x-3y=x^2\left(x-y\right)+3\left(x-y\right)=\left(x-y\right)\left(x^2+3\right)\)
\(x^3-2x^2-4xy^2+x=x\left(x^2-2x+1-4y^2\right)=x\left[\left(x-1\right)^2-\left(2y\right)^2\right]=x\left(x+2y-1\right)\left(x-2y-1\right)\)
\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-8=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-8\)
Đặt \(x^2+7x+10=t\), ta có:
\(t\left(t+2\right)-8=t^2+2t-8=t^2-2t+4t-8=t\left(t-2\right)+4\left(t-2\right)=\left(t-2\right)\left(t+4\right)\)
\(=\left(x^2+7x+10+4\right)\left(x^2+7x+10-2\right)=\left(x^2+7x+14\right)\left(x^2+7x-8\right)\)
Câu 1:
$(2x^2-3)(x+5)=2x^2(x+5)-3(x+5)=2x^3+10x^2-3x-15$
Câu 2:
a.
$(x+3)^2=x^2+2.x.3+3^2=x^2+6x+9$
b.
$y^2-25=y^2-25$
\(1.5x\left(x^2+2x-1\right)-3x^2\left(x-2\right)=5x^3+10x^2-5x-3x^3+6x^2\)
\(=2x^3+16x^2-5x\)
\(=\left(2x^3-x\right)+\left(16x^2-4x\right)\)
\(=x\left(2x^2-1\right)+4x\left(4x-1\right)\left(ĐCCM\right)\)
1.
\(3x^2-3xy+5x-5y\)
\(=\left(3x^2-3xy\right)+\left(5x-5y\right)\)
\(=3x.\left(x-y\right)+5.\left(x-y\right)\)
\(=\left(x-y\right).\left(3x+5\right)\)
2.
\(x^2+y^2+2xy-x-y\)
\(=\left(x^2+2xy+y^2\right)-\left(x+y\right)\)
\(=\left(x+y\right)^2-\left(x+y\right)\)
\(=\left(x+y\right).\left(x+y-1\right)\)
3.
\(x^2-xy+x-y\)
\(=\left(x^2-xy\right)+\left(x-y\right)\)
\(=x.\left(x-y\right)+\left(x-y\right)\)
\(=\left(x-y\right).\left(x+1\right)\)
4.
\(x^2-2xy+y^2-z^2+2zt-t^2\)
\(=\left(x^2-2xy+y^2\right)-\left(z^2-2zt+t^2\right)\)
\(=\left(x-y\right)^2-\left(z-t\right)^2\)
\(=\left[x-y-\left(z-t\right)\right].\left[x-y+\left(z-t\right)\right]\)
\(=\left(x-y-z+t\right).\left(x-y+z-t\right)\)
6.
\(2x^2-8x+6\)
\(=2.\left(x^2-4x+3\right)\)
\(=2.\left(x^2-3x-x+3\right)\)
\(=2.\left[\left(x^2-3x\right)-\left(x-3\right)\right]\)
\(=2.\left[x.\left(x-3\right)-\left(x-3\right)\right]\)
\(=2.\left(x-3\right).\left(x-1\right)\)
Chúc bạn học tốt!