a) \(x\left(x^2-16\right)-\left(x^2+1\right)\left(x-1\right)\) =\(x^3-16x^2-x^3+x^2-x+1\)
= \(x^2-17x+1\)
b) \(\left(y^2-9\right)\left(y^2+9\right)-\left(y^4-4\right)\) = \(\left(y^4-81\right)-\left(y^4-16\right)\)
=\(-65\)
1. Viết biểu thức dưới dạng bình phương của một tổng
\(2xy^2+x^2y^4+1\)
2, Rút gọn biểu thức :
a, \(2\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2+\left(x-y\right)^2\)
b, \(\left(x-y+z\right)^2+\left(z-y\right)^2+2\left(x-y+z\right)\left(y-z\right)\)
Tính
a) \(\left(x+3\right).\left(x^2-3x+9\right)-x.\left(x-2\right)\left(x+2\right)\)
b) \(\left(x+y\right)^3-x.\left(x+3y\right)^2+y\left(y-3x\right)^2\)
Rút gọn : \(\frac{1}{\left(x+y\right)^3}.\left(\frac{1}{x^3}+\frac{1}{y^3}\right)+\frac{3}{\left(x+y\right)^5}\left(\frac{1}{x^2}+\frac{1}{y^2}\right)+\frac{6}{\left(x+y\right)^5}\left(\frac{1}{x}+\frac{1}{y}\right)\)
rút gọn
a)\(\left(7x-8\right).\left(7x+8\right)-10.\left(2x+3\right)^2+5x.\left(3x-2\right)^24x.\left(x-5\right)^2\)
b) \(\left(3x+7\right)^3-\left(5x-y\right).\left(25x^2+5xy+y^2\right)+\left(x+2y\right)^3\)
a) Tìm x,y biết: x4+x2-y2+y+10=0
b) Tính giá trị biểu thức: \(\frac{\left(1+\frac{1}{4}\right)\left(3^4+\frac{1}{4}\right)\left(5^4+\frac{1}{4}\right)...\left(29^4+\frac{1}{4}\right)}{\left(2^4+\frac{1}{4}\right)\left(4^4+\frac{1}{4}\right)\left(6^4+\frac{1}{4}\right)...\left(30^4+\frac{1}{4}\right)}\)
Chứng minh :
a) \(\left(x-1\right)\left(x^2+x+1\right)=x^3-1\)
b) \(\left(x^3+x^2y+xy^2+y^3\right)\left(x-y\right)=x^4-y^4\)
Tinh
a) \(\left(x+y\right)^3+\left(y-x\right)^3\)
b) \(\left(x+3\right).\left(x^2-3x+9\right)-x.\left(x-2\right).\left(x+2\right)\)
Phân tích đa thức thành nhân tử :
\(a,\left(x+y\right)^5-x^5-y^5\)
\(b,\left(x^2+y^2\right)^3+\left(z^2-x^2\right)^3+\left(y^2+z^2\right)^3\)
\(c,x^9-x^7-x^6-x^5+x^4+x^3+x^2+1\).
Rút gọn
\(\left(3x+y\right)^3-\left(5x-y\right).\left(25x^2+5xy+y^2\right)+\left(x+2y\right)^3\)