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- Toán lớp 8
Khóa học Toán lớp 8
Gửi câu trả lời của bạn
a) \(4x^2-6x=2x\left(2x-3\right)\)
b) \(9x^4y^3+3x^2y^4=3x^2y^3\left(3x^2+y\right)\)
c) \(3\left(x-y\right)-5x\left(y-x\right)=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(5x+3\right)\left(x-y\right)\)
d) \(x^3-2x^2+5x=x\left(x^2-2x+5\right)\)
e) \(5\left(x+3y\right)-15x\left(x+3y\right)=\left(5-15x\right)\left(x+3y\right)\)
\(=5\left(1-3x\right)\left(x+3y\right)\)
f) \(2x^2\left(x+1\right)-4\left(x+1\right)=\left(2x^2-4\right)\left(x+1\right)\)
\(=\left(\sqrt{2}x-2\right)\left(\sqrt{2}x+2\right)\left(x+1\right)\)
Bài 2:
a) \(x^2-y^2+3x-3y=\left(x^2-y^2\right)+\left(3x-3y\right)\)
\(=\left(x-y\right)\left(x+y\right)+3\left(x-y\right)=\left(x-y\right)\left(x+y+3\right)\)
b) \(5x-5y+x^2-2xy+y^2=\left(5x-5y\right)+\left(x^2-2xy+y^2\right)\)
\(=5\left(x-y\right)+\left(x-y\right)^2=\left(x-y\right)\left(x-y+5\right)\)
c) \(x^2-5x+4=x^2-x-4x+4=\left(x^2-x\right)-\left(4x-4\right)\)
\(=x\left(x-1\right)-4\left(x-1\right)=\left(x-1\right)\left(x-4\right)\)
\(\text{a)}x^3-6x^2+12x-8\)
\(=x^3-2x^2-4x^2+8x+4x-8\)
\(=\left(x^3-2x^2\right)-\left(4x^2-8x\right)+\left(4x-8\right)\)
\(=x^2\left(x-2\right)+4x\left(x-2\right)+4\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+4x+4\right)\)
\(=\left(x-2\right)\left(x+2\right)^2\)
\(\text{b)}8x^2+12x^2y+6xy^2+y^3=\left(2x+y\right)^3\)
Bài 2:
\(\text{a) }x^7+1=\left(x^{\frac{7}{3}}\right)^3+1^3=\left(x^{\frac{7}{3}}+1\right)\left[\left(x^{\frac{7}{3}}\right)^2-x^{\frac{7}{3}}+1\right]=\left(x^{\frac{7}{3}}+1\right)\left(x^{\frac{14}{3}}-x^{\frac{7}{3}}+1\right)\)
\(\text{b) }x^{10}-1=\left(x^5\right)^2-1^2=\left(x^5-1\right)\left(x^5+1\right)\)
Bài 3:
\(\text{a) }69^2-31^2=\left(69-31\right)\left(69+31\right)=38.100=3800\)
\(\text{b) }1023^2-23^2=\left(1023-23\right)\left(1023+23\right)=1000.1046=1046000\)
\(x^3+2x^2y+xy^2-9x\)
\(=\)\(x\left[\left(x^2+2xy+y^2\right)-9\right]\)
\(=\)\(x\left[\left(x+y\right)^2-9\right]\)
\(=\)\(x\left(x+y-3\right)\left(x+y+3\right)\)
Chúc bạn học tốt ~
Phùng Minh Quân sai rồi nhé!Nhưng theo như lời hứa giữa hai ta,nên t sẽ không tích sai nhá!
\(x^3-2x^2y+xy^2-9x\)
\(=xy^2-x^2y-3xy-x^2y+x^3+3x^2+3xy-3x^2-9x\)
\(=xy\left(y-x-3\right)-x^2\left(y-x-3\right)+3x\left(y-x-3\right)\)
\(=\left(y-x-3\right)\left(xy-x^2+3x\right)\)
\(=x\left(y-x-3\right)\left(y-x+3\right)\)
HIHI, bài này thì bó tay lẫn cả chân
Vì mới học xong lớp 6 hoi.
Học tốt nha, nếu ko ai giải thì thử vào câu hỏi tương tự thử
Nha, học tốt !
#)Giải:
-Không sao mình biết cách làm mà, mình chỉ thử lòng ae thui !
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a) \(x^2-y^2-x-y\)
\(=\left(x^2-y^2\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-1\right)\)
b) \(x^2-y^2+2yz-z^2\)
\(=x^2-\left(y^2-2yz+z^2\right)\)
\(=x^2-\left(y-z\right)^2\)
\(=\left(x-y+z\right)\left(x+y-z\right)\)
Bài 1:
a) \(x^3-5x^2+8x-4\)
\(=x^3-4x^2+4x-x^2+4x-4\) \(=x\left(x^2-4x+4\right)-\left(x^2-4x+4\right)\)\(=\left(x-1\right)\left(x-2\right)^2\)
b) Ta có: \(\frac{A}{M}=\frac{10x^2-7x-5}{2x-3}=5x+4+\frac{7}{2x-3}\)
Với \(x\in Z\)thì \(A⋮M\)khi \(\frac{7}{2x-3}\in Z\)\(\Rightarrow7⋮\left(2x-3\right)\)\(\Rightarrow2x-3\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)
\(\Rightarrow=\left\{1;5;\pm2\right\}\)thì khi đó \(A⋮M\)
Các bài làm này có đúng ko ạ, ai đó duyệt giúp em, em cảm ơn.
Bài 1:
a)x3-5x2+8x-4=x3-4x2+4x-x2+4x-4
=x(x2-4x-4)-(x2-4x+4)
=(x-1) (x-2)2
b)Xét:
\(\frac{a}{b}-\frac{10x^2-7x-5}{2x-3}\)
=\(5x+4+\frac{7}{2x-3}\)
Với x thuộc Z thì A /\ B khi \(\frac{7}{2x-3}\) thuộc Z => 7 /\ (2x-3)
Mà Ư(7)={-1;1;-7;7} => x=5;-2;2;1 thì A /\ B
c)Biến đổi \(\frac{x}{y^3-1}-\frac{x}{x^3-1}=\frac{x^4-x-y^4+y}{\left(y^3-1\right)\left(x^3-1\right)}\)
=\(\frac{\left(x^4-y^4\right)\left(x-y\right)}{xy\left(y^2+y+1\right)\left(x^2+x+1\right)}\)(do x+y=1=>y-1=-x và x-1=-y)
=\(\frac{\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)-\left(x-y\right)}{xy\left[x^2y^2+y^2x+y^2+xy^2+xy+y+x^2+x+1\right]}\)
=\(\frac{\left(x-y\right)\left(x^2+y^2-1\right)}{xy\left[x^2y^2+xy\left(x+y\right)+x^2+y^2+xy+2\right]}\)
=\(\frac{\left(x-y\right)\left(x^2-x+y^2-y\right)}{xy\left[x^2y^2+\left(x+y\right)^2+2\right]}=\frac{\left(x-y\right)\left[x\left(x-1\right)+y\left(y-1\right)\right]}{xy\left(x^2y^2+3\right)}\)
=\(\frac{\left(x-y\right)\left[x\left(-y\right)+y\left(-x\right)\right]}{xy\left(x^2y^2+3\right)}=\frac{\left(x-y\right)\left(-2xy\right)}{xy\left(x^2y^2+3\right)}\)
=\(\frac{-2\left(x-y\right)}{x^2y^2+3}\)Suy ra điều phải chứng minh
Bài 2 )
a)(x2+x)2+4(x2+x)=12 đặt y=x2+x
y2+4y-12=0 <=>y2+6y-2y-12=0
<=>(y+6)(y-2)=0 <=> y=-6;y=2
>x2+x=-6 vô nghiệm vì x2+x+6 > 0 với mọi x
>x2+x=2 <=> x2+x-2=0 <=> x2+2x-x-2=0
<=>x(x+2)-(x+2)=0 <=>(x+2)(x-1) <=> x=-2;x-1
Vậy nghiệm của phương trình x=-2;x=1
b)\(\frac{x+1}{2008}+\frac{x+2}{2007}+\frac{x+3}{2006}+\frac{x+4}{2005}+\frac{x+5}{2004}\)\(+\frac{x+6}{2003}\)
=\(\left(\frac{x+1}{2008}+1\right)+\left(\frac{x+2}{2007}+1\right)+\left(\frac{x+3}{2006}+1\right)+\left(\frac{x+4}{2005}+1\right)\)\(+\left(\frac{x+5}{2004}+1\right)+\left(\frac{x+6}{2003}+1\right)\)
<=>\(\frac{x+2009}{2008}+\frac{x+2009}{2007}+\frac{x+2009}{2006}-\frac{x+2009}{2005}\)\(+\frac{x+2009}{2004}+\frac{x+2009}{2003}\)
<=>\(\frac{x+2009}{2008}+\frac{x+2009}{2007}+\frac{x+2009}{2006}\)\(-\frac{x+2009}{2005}-\frac{x+2009}{2004}-\frac{x+2009}{2003}=0\)
Nhờ OLM xét giùm em vs ạ !
Bài 1
\(a,5x^2-10xy+5y^2\)
\(=5\cdot\left(x^2-2xy+y^2\right)\)
\(=5\cdot\left(x-y\right)^2\)
\(b,x^2-y^2+6y-9\)
\(=x^2-\left(y^2-6y+9\right)\)
\(=x^2-\left(y-3\right)^2\)
\(=\left(x-y+3\right)\cdot\left(x+y-3\right)\)
\(c,3x^4-75x^2y^2\)
\(=3x^2\cdot\left(x^2-25y^2\right)\)
\(=3x^2\cdot\left(x-5y\right)\cdot\left(x+5y\right)\)
\(d,x^4y+xy^4\)
\(=xy\left(x^3+y^3\right)\)
\(=xy\cdot\left(x+y\right)\cdot\left(x^2-xy+y^2\right)\)