Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(x^4+64\)
\(=\left(x^2\right)^2+8^2+2x^2.8-2x^2.8\)
\(=\left(x^2+8\right)^2-\left(4x^2\right)\)
\(=\left(x^2-4x+8\right)\left(x^2+4x+8\right)\)
= ( x 4) 2 + 82 - 16x4 + 16x4 = ( x4 + 4) - ( 4x ) 2 = ( x4 +4 - 4x)( x4 +4 + 4x )
=
( x4 ) 2 + 16x4 + 16x4 = ( x4 + ) 2 = ( x4 + 4 - 4x ) + ( x4 + 4 + 4x )
Đáp số : ....
f) \(x^2-6x+5=\left(x^2-x\right)+\left(-5x+5\right)=x\left(x-1\right)-5\left(x-1\right)=\left(x-1\right)\left(x-5\right)\)
g) \(x^4+64=\left(x^2+4x+8\right)\left(x^2-4x+8\right)\)
\(x^2-6x+5\)
\(=\left(x^2-2.3x+3^2\right)-4\)
\(=\left(x-3\right)^2-2^2\)
\(=\left(x-3-2\right)\left(x-3+2\right)\)
\(=\left(x-5\right)\left(x-1\right)\)
\(a,\frac{1}{64}x^6-125y^3\)
\(=\left(\frac{1}{2}x\right)^6-\left(5y\right)^3\)
\(=\left(\frac{1}{4}x^2\right)^3-\left(5y\right)^3\)
\(\left(\frac{1}{4}x^2-5y\right)\left[\left(\frac{1}{4}x^2\right)^2+\left(\frac{1}{4}x^2\right).5y+25y^2\right]\)
\(b,27a^3-54a^2b+36ab^2-8b^3\)
\(=\left(3a\right)^3-3.2.\left(3a\right)^2b+3.3a.\left(2b\right)^2-\left(2b\right)^3\)
\(=\left(3a-2b\right)^3\)
\(c,x^6-x^6\)
\(=0\)
\(d,10x-25-x^2\)
\(=-x^2+10x-25\)
\(=-\left(x^2-10x+25\right)\)
\(=-\left(x-5\right)^2\)
Bạn tham khảo link này nhé :
https://olm.vn/hoi-dap/detail/11579055142.html
~Study well~
#SJ
\(a,\)\(x^{16}-1\)
\(=\left(x^8+1\right)\left(x^8-1\right)\)
\(=\left(x^8+1\right)\left(x^4+1\right)\left(x^4-1\right)\)
\(=\left(x^8+1\right)\left(x^4+1\right)\left(x^2+1\right)\left(x^2-1\right)\)
\(=\left(x^8+1\right)\left(x^4+1\right)\left(x^2+1\right)\left(x+1\right)\left(x-1\right)\)
Ta có : \(x^3-64\)
\(=x^3-4^3\)
Áp dung hằng dẳng thức : \(a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\)
\(\Rightarrow x^3-4^3=\left(x-4\right)\left(x^2+4x+4^2\right)\)
\(x^3\)\(-64\)\(=x^3\)\(-4^3\)=\(\left(x-4\right)\)\(\left(x^2+4x+16\right)\)