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a) \(x^2-25-4xy+4y^2\)
\(=\left(x^2-4xy+4y^2\right)-25\)
\(=\left(x-2y\right)^2-5^2\)
\(=\left(x-2y-5\right)\left(x-2y+5\right)\)
b) \(x^2-8x+15\)
\(=x^2-3x-5x+15\)
\(=x\left(x-3\right)-5\left(x-3\right)\)
\(=\left(x-3\right)\left(x-5\right)\)
a)\(x^2-25-4xy+4y^2\Leftrightarrow\left(x^2-4xy+4y^2\right)-25\)
\(\Leftrightarrow\left(x-2y\right)^2-5^2\)
\(\Leftrightarrow\left(x-2y-5\right)\left(x-2y+5\right)\)
b)\(x^2-8x+15\Leftrightarrow\left(x-3\right)\left(x-5\right)\)
\(a,6x^2-9x=3x\left(x-3\right)\)
\(b,x^3-2x^2-3x+6\)
\(=\left(x^3-2x^2\right)-\left(3x-6\right)\)
\(=x^2\left(x-2\right)-3\left(x-2\right)\)
\(=\left(x^2-3\right)\left(x-2\right)\)
\(e,2x\left(x-y\right)-3y\left(x-y\right)\)
\(=\left(2x-3y\right)\left(x-y\right)\)
a) 6x2 - 9x
= 3x (2x - 3)
b) x3 - 2x2 - 3x + 6
= x2(x - 2) - 3 (x - 2)
=(x - 2) (x2 - 3)
c) x2 - 4x + 4 - 9y2
= (x - 2)2 - 9y2
=(x - 2 - 3y)(x - 2 + 3y)
e) 2x(x - y) - 3y(x - y)
= (x - y)(2x - 3y)
xin lỗi mình học ngu nên không biết làm nhìu nha
Bài làm:
1) Ta có: \(2x^2+5xy+2y^2\)
\(=\left(2x^2+4xy\right)+\left(xy+2y^2\right)\)
\(=2x\left(x+2y\right)+y\left(x+2y\right)\)
\(=\left(2x+y\right)\left(x+2y\right)\)
2) Ta có: \(2x^2+2xy-4y^2\)
\(=\left(2x^2-2xy\right)+\left(4xy-4y^2\right)\)
\(=2x\left(x-y\right)+4y\left(x-y\right)\)
\(=2\left(x+2y\right)\left(x-y\right)\)
\(1)2x^2+5xy+2y^2=2x^2+4xy+xy+2y^2=\left(2x^2+4xy\right)+\left(xy+2y^2\right)=2x\left(x+2y\right)+y\left(x+2y\right)=\left(2x+y\right)\left(x+2y\right)\)\(2)2x^2+2xy-4y^2=2x^2+4xy-2xy-4y^2=\left(2x^2-2xy\right)+\left(4xy-4y^2\right)=2x\left(x-y\right)+4y\left(x-y\right)=\left(2x+4y\right)\left(x-y\right)\)
Gợi ý:
a) Đặt \(x^2+3x+1=a\)
b) \(\left(x^2+8x+7\right)\left(x+3\right)\left(x+5\right)+15\)
\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)
Đặt \(x^2+8x+11=a\)
c) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)
Đặt \(x^2+7x+11=a\)
d) \(\left(4x+1\right)\left(12x-1\right)\left(3x+2\right)\left(x+1\right)-4=\left(12x^2+11x+2\right)\left(12x^2+11x-1\right)-4\)
Đặt \(12x^2+11x-1=a\)
Câu hỏi của Nguyễn Tấn Phát - Toán lớp 8 - Học toán với OnlineMath
Em tham khảo câu e nhé!
1. \(4x^2-2x-3y-9y^2\)
\(=\left(2x\right)^2-\left(3y\right)^2-\left(2x+3y\right)\)
\(=\left(2x-3y\right)\left(2x+3y\right)-\left(2x+3y\right)\)
\(=\left(2x+3y\right)\left(2x-3y-1\right)\)
2. \(x^2-25=6x-9\)
\(\Rightarrow x^2-6x+9=25\)
\(\Rightarrow\left(x-3\right)^2=25\)
\(\Rightarrow\orbr{\begin{cases}x-3=5\\x-3=-5\end{cases}}\Rightarrow\orbr{\begin{cases}x=8\\x=-2\end{cases}}\)
a, \(9x^2+6xy+y^2=\left(3x\right)^2+2\times3xy+y^2=\left(3x+y\right)^2\)
b, \(6x-9-x^2=-\left(x^2-2\times3x+3^2\right)=-\left(x-3\right)^2\)
c, \(x^2+4y^2+4xy=x^2+2\times2xy+\left(2y\right)^2=\left(x+2y\right)^2\)
1, \(=\left(2y\right)^2-\left(x^2-2x+1\right)=\left(2y\right)^2-\left(x-1\right)^2=\left(2y-x+1\right)\left(2y+x-1\right)\)
2, \(=2\left(x^2-y^2\right)+8\left(x+1\right)=2\left(x+1\right)\left(x-1\right)+8\left(x+1\right)=2\left(x+1\right)\left(x-1+4\right)=2\left(x+1\right)\left(x+3\right)\)
3, \(=\left(x^2+6x+9\right)-\left(2y\right)^2=\left(x+3\right)^2-\left(2y\right)^2=\left(x+3-2y\right)\left(x+3+2y\right)\)
4, \(=\left(x+y\right)^2-1=\left(x+y-1\right)\left(x+y+1\right)\)
\(4y^2-x^2+2x-1\)
\(=4y^2-\left(x^2-2x+1\right)\)
\(=\left(2y\right)^2-\left(x-1\right)^2\)
\(=\left(2y-x+1\right)\left(2y+x-1\right)\)
hk tốt
^^
\(8x^3-12x^2+6x-9\\ =4x^2\left(2x-3\right)+3\left(2x-3\right)\\ =\left(2x-3\right)\left(4x^2+3\right)\)
\(-x^2+9x-1+4y^2\\ =-\left(x^2-9x+1-4y^2\right)\)