Bài `1`

\(a,5x^2-10xy=5x\left(x-2y\right)\\ b,3x\left(x-y\right)-6\left(x-y\right)=\left(x-y\right)\left(3x-6\right)\\ =3\left(x-y\right)\left(x-2\right)\\ c,2x\left(x-y\right)-4y\left(y-x\right)=2x\left(x-y\right)+4y\left(x-y\right)\\ =\left(x-y\right)\left(2x+4y\right)=2\left(x-y\right)\left(x+2y\right)\\ d,9x^2-9y^2=\left(3x\right)^2-\left(3y\right)^2=\left(3x-3y\right)\left(3x+3y\right)\\ f,xy-xz-y+z=\left(xy-xz\right)-\left(y-z\right)\\ =x\left(y-z\right)-\left(y-z\right)=\left(y-z\right)\left(x-1\right)\)

Bài `3`

\(a,3x^2+8x=0\\ \Leftrightarrow x\left(3x+8\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\3x+8=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\3x=-8\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{8}{3}\end{matrix}\right.\)

\(b,9x^2-25=0\\ \Leftrightarrow\left(3x\right)^2-5^2=0\\ \Leftrightarrow\left(3x-5\right)\left(3x+5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}3x-5=0\\3x+5=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}3x=5\\3x=-5\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{3}\\x=-\dfrac{5}{3}\end{matrix}\right.\)

\(c,x^3-16x=0\\ \Leftrightarrow x\left(x^2-16\right)=0\\ \Leftrightarrow x\left(x-4\right)\left(x+4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x-4=0\\x+4=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)

\(d,x^3+x=0\\ \Leftrightarrow x\left(x^2+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x^2+1\in\varnothing\\x=0\end{matrix}\right.\Rightarrow x=0\)

Lời giải:
a. $5x^2-10xy=5x(x-2y)$

b. $3x(x-y)-6(x-y)=(x-y)(3x-6)=3(x-y)(x-2)$
c. $2x(x-y)-4y(y-x)=2x(x-y)+4y(x-y)=(x-y)(2x+4y)=2(x-y)(x+2y)$

d. $9x^2-9y^2=9(x^2-y^2)=9(x-y)(x+y)$

e. $x^2-xy-x+y=(x^2-xy)-(x-y)=x(x-y)-(x-y)=(x-y)(x-1)$

f. $xy-xz-y+z=(xy-y)-(xz-z)=y(x-1)-z(x-1)=(x-1)(y-z)$

a) =( x²+y²-5)²-[2(xy-2)]²

⁼( x²+y²-5)²- (2xy-4)²

=(x²+y²-5+2xy-4)(x²+y²-5-2xy+4)

=[(x+y)²-9][(x-y)²-1]

phân tích tiếp HĐT 2 ở 2 thừa số

2)Tính nhanh:

a)\(202^2-54^2+256.352\)

​\(=\left(202-54\right)\left(202+54\right)+256.352\)​

\(=148.256+256.352\)

\(=256\left(148+352\right)\)

\(=256.500\)

\(=128000\)

b)\(621^2-769.373-148^2\)

\(=621^2-148^2-769.373\)

\(=\left(621-148\right)\left(621+148\right)-769.373\)

\(=473.769-769.373\)

\(=769\left(473-373\right)\)

\(=769.100\)

\(=76900\)

\(a,\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)

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

\(=\left(-x-4y+5\right)\left(3x+2y+3\right)\)

\(b,9x^2+90x+225-\left(x-7\right)^2\)

\(=9\left(x^2+10x+25\right)-\left(x-7\right)^2\)

\(=9\left(x+5\right)^2-\left(x-7\right)^2\)

\(=\left[3\left(x+5\right)\right]^2-\left(x-7\right)^2\)

\(=\left(3x+15\right)^2-\left(x-7\right)^2\)

\(=\left(3x+15-x+7\right)\left(3x+15+x-7\right)\)

\(=\left(2x+22\right)\left(4x+8\right)\)

\(=2\left(x+11\right).4\left(x+2\right)\)

\(=8\left(x+2\right)\left(x+11\right)\)

\(c,49\left(y-4\right)^2-9y^2-36y-36\)

\(=\left\{\left[7\left(y-4\right)\right]^2-\left(3y\right)^2\right\}-\left(36y+36\right)\)

\(=\left(7y-28-3y\right)\left(7y-28+3y\right)-36\left(y+1\right)\)

\(=\left(4y-28\right)\left(10y-28\right)-36\left(y+1\right)\)

\(=4\left(y-7\right)2\left(5y-14\right)-36\left(y+1\right)\)

\(=8\left(y-7\right)\left(5y-14\right)-36\left(y+1\right)\)

\(=4\left[2\left(y-7\right)\left(5y-14\right)-9\left(y+1\right)\right]\)

mk ko chắc là câu này mk lm đg

\(d,x^2-5x-14\)

\(=x^2+2x-7x-14\)

\(=x\left(x+2\right)-\left(7x+14\right)\)

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

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

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

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

\(=\left(3x+2y+3\right)\left(-x-4y+5\right)\)

\(49\left(y-4\right)^2-9y^2-36y-36\)

\(=49\left(y-4\right)^2-\left(9y^2+36y+36\right)\)

\(=49\left(y-4\right)^2-\left(3y+6\right)^2\)

\(=[7\left(y-4\right)]^2-\left(3y+6\right)^2\)

\(=\left(7y-28\right)^2-\left(3y+6\right)^2\)

\(=\left(7y-28+3y+6\right)\left(7y-28-3y-6\right)\)

\(=\left(10y-22\right)\left(4y-34\right)\)

\(9x^2+90x+225-\left(x-7\right)^2\)

\(=\left(3x+15\right)^2-\left(x-7\right)^2\)

\(=\left(3x+15+x-7\right)\left(3x+15-x+7\right)\)

\(=\left(4x+8\right)\left(2x+22\right)\)

a: A=y(x-4)-5(x-4)

=(x-4)(y-5)

Khi x=14 và y=5,5 thì A=(14-4)(5,5-5)=0,5*10=5

b: \(B=x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\)

Khi x=5,2 và y=4,8 thì B=(5,2+4,8)(5,2-5)

=0,2*10=2

d: Khi x=5,75 và y=4,25 thì

D=5,75^3-5,75^2*4,25+4,25^3

=8087/64

a: A=yx-4y-5x+20

=y(x-4)-5(x-4)

=(x-4)(y-5)

Khi x=14 và y=5,5 thì A=(14-4)(5,5-5)=0,5*10=5

b: \(B=x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\)

Khi x=5,2 và y=4,8 thì B=(5,2+4,8)(5,2-5)

=0,2*10=2

d: Khi x=5,75 và y=4,25 thì

D=5,75^3-5,75^2*4,25+4,25^3

=8087/64

c: \(D=xyz-xy-yz-xz+x+y+z-1\)

=xy(z-1)-yz+y-xz+z+x-1

=xy(z-1)-y(z-1)-z(x-1)+(x-1)

=(z-1)(xy-y)-(x-1)(z-1)

=(z-1)(xy-y-1)

=(11-1)(9*10-10-1)

=10*79=790