Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(x^3-x^2-21x+45\)
\(=\left(x^3-3x^2\right)+\left(2x^2-6x\right)+\left(-15x+45\right)\)
\(=x^2\left(x-3\right)+2x\left(x-3\right)-15\left(x-3\right)\)
\(=\left(x^2+2x-15\right)\left(x-3\right)\)
\(=\left[\left(x^2-3x\right)+\left(5x-15\right)\right]\left(x-3\right)\)
\(=\left[x\left(x-3\right)+5\left(x-3\right)\right]\left(x-3\right)\)
\(=\left(x+5\right)\left(x-3\right)^2\)
\(\left(x+y+z\right)^3-x^3-y^3-z^3.\)
\(=x^3+y^3+z^3+3\left(x+y\right)\left(x+z\right)\left(y+z\right)-x^3-y^3-z^3\)
\(=3\left(x+y\right)\left(x+z\right)\left(y+z\right)\)
~ Chúc bạn học tốt~
bài 1 : \(a^2-b^2-4ab+4\)
\(=\left(a-b\right)\left(a+b\right)-4\left(ab-1\right)\)
a) \(x^2+4x-y^2+4\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2-y\right)\left(x+2+y\right)\)
c) \(x^2-2xy+y^2-z^2+2zt-t^2\)
\(=\left(x-y\right)^2-\left(z-t\right)^2\)
\(=\left(x-y-z+t\right)\left(x-y+z-t\right)\)
a) Đưa về hằng đẳng thức số 3 , ta có :
\(\left(x^2+1\right)^2-4x^2\)
\(=\left(x^2+1\right)^2-\left(2x\right)^2\)
\(=\left(x^2-1-2x\right)\left(x^2-1+2x\right)\)
b) \(x^2-y^2+2yz-z^2\)
\(=x^2-\left(y^2-2yz+z^2\right)\)
\(=x^2-\left(y-z\right)^2\)
Tương tự như câu a , áp dụng hằng số 3 , ta có :
\(=x^2-\left(y-z\right)^2=\left(x-y+z\right)\left(x+y-z\right)\)
1) \(\left(x^2+1\right)^2-4x^2\)
\(=\left(x^2+1\right)^2-\left(2x\right)^2\)
\(=\left(x^2+2x+1\right)\left(x^2-2x+1\right)\)
\(=\left(x+1\right)^2\left(x-1\right)^2\)
\(=\left(x^2-1\right)\left(x^2-1\right)\)
\(=\left(x^2-1\right)^2\)
\(=x^5-x^2+\left(x^2+x+1\right)\)
\(=x^2\left(x^3-1\right)+\left(x^2+x+1\right)\)
\(=x^2\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^3-x^2\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^3-x^2+1\right)\left(x^2+x+1\right)\)
ta muốn làm nắm nhưng mi bợi thêm năm nữa đi nha đợi ta lên lớp 8 ta giải cho
\(x^2\) - \(x\) - 121
= (\(x^2\) - \(2.x.\frac{1}{2}\) + \(\frac{1}{4}\) ) - \(\frac{1}{4}\) - 121
= (\(x\) - \(\frac{1}{2}\) )2 - \(\frac{485}{4}\)
= (\(x\) - \(\frac{1}{2}\) - \(\frac{\sqrt{485}}{2}\) ) (\(x\) - \(\frac{1}{2}\) + \(\frac{\sqrt{485}}{2}\) )
= (\(x\) - \(\frac{1+\sqrt{485}}{2}\) ) (\(x\) - \(\frac{1-\sqrt{485}}{2}\) )
\(x^2-x-121\)
\(=\left(x^2-2.x.\frac{1}{2}+\frac{1}{4}\right)-\frac{1}{4}-121\)
\(=\left(x-\frac{1}{2}\right)^2-\frac{485}{4}\)
\(=\left(x-\frac{1}{2}-\frac{\sqrt{485}}{2}\right)\left(x-\frac{1}{2}+\frac{\sqrt{485}}{2}\right)\)
\(=\left(x-\frac{1+\sqrt{485}}{2}\right)\left(x-\frac{1-\sqrt{485}}{2}\right)\)