![](https://rs.olm.vn/images/avt/0.png?1311)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=x+x^2-x^3+x^4-x^5+2+2x-2x^2+2x^3-2x^4-\left(1+x+x^2+x^3+x^4-x-x^2-x^3-x^4-x^5\right)\\ =2+3x-x^2+x^3-x^4-x^5-1\\ =-x^5-x^4+x^3-x^2+3x+1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bạn cần viết đầy đủ đề: Bao gồm yêu cầu đề và công thức toán để được hỗ trợ tốt hơn.
\(D=\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^4-x^2+1\right)\left(x^8-x^4+1\right)\)
\(=\left[\left(x^2+1\right)^2-x^2\right]\left(x^4-x^2+1\right)\left(x^8-x^4+1\right)\)
\(=\left(x^4+x^2+1\right)\left(x^4-x^2+1\right)\cdot\left(x^8-x^4+1\right)\)
\(=\left(x^8+2x^4+1-x^4\right)\left(x^8-x^4+1\right)\)
\(=\left(x^8+1\right)^2-x^8\)
\(=x^{16}+x^8+1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Dễ
Thế
Mà
Cũnhoir
Dc
Ạ
Chịu
Chắc
Phải
Ngu
Lamqs
Mới
Hỏi
Câu
Này
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\left(x+1\right)\left(x-1\right)\)
\(=x^2-1^2\)
\(=x^2-1\)
b) \(\left(x+1\right)\left(x-1\right)\left(x^2+1\right)\)
\(=\left(x^2-1\right)\left(x^2+1\right)\)
\(=\left(x^2\right)^2-1^2\)
\(=x^4-1\)
c) \(\left(x+1\right)\left(x-1\right)\left(x^2+1\right)\left(x^2+1\right)-x^8\)
\(=\left(x^2-1\right)\left(x^2+1\right)\left(x^4+1\right)-x^8\)
\(=\left(x^4-1\right)\left(x^4+1\right)-x^8\)
\(=\left(x^4\right)^2-1-x^8\)
\(=x^8-1-x^8\)
\(=-1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
`@` `\text {Ans}`
`\downarrow`
`a)`
Thu gọn:
`P(x)=`\(5x^4 + 3x^2 - 3x^5 + 2x - x^2 - 4 +2x^5\)
`= (-3x^5 + 2x^5) + 5x^4 + (3x^2 - x^2) + 2x - 4`
`= -x^5 + 5x^4 + 2x^2 + 2x - 4`
`Q(x) =`\(x^5 - 4x^4 + 7x - 2 + x^2 - x^3 + 3x^4 - 2x^2\)
`= x^5 + (-4x^4 + 3x^4) - x^3 + (x^2 - 2x^2) + 7x - 2`
`= x^5 - x^4 - x^3 - x^2 + 7x - 2`
`@` Tổng:
`P(x)+Q(x)=`\((-x^5 + 5x^4 + 2x^2 + 2x - 4) + (x^5 - x^4 - x^3 - x^2 + 7x - 2)\)
`= -x^5 + 5x^4 + 2x^2 + 2x - 4 + x^5 - x^4 - x^3 - x^2 + 7x - 2`
`= (-x^5 + x^5) - x^3 + (5x^4 - x^4) + (2x^2 - x^2) + (2x + 7x) + (-4-2)`
`= 4x^4 - x^3 + x^2 + 9x - 6`
`@` Hiệu:
`P(x) - Q(x) =`\((-x^5 + 5x^4 + 2x^2 + 2x - 4) - (x^5 - x^4 - x^3 - x^2 + 7x - 2)\)
`= -x^5 + 5x^4 + 2x^2 + 2x - 4 - x^5 + x^4 + x^3 + x^2 - 7x + 2`
`= (-x^5 - x^5) + (5x^4 + x^4) + x^3 + (2x^2 + x^2) + (2x - 7x) + (-4+2)`
`= -2x^5 + 6x^4 + x^3 + 3x^2 - 5x - 2`
`b)`
`@` Thu gọn:
\(H (x) = ( 3x^5 - 2x^3 + 8x + 9) - ( 3x^5 - x^4 + 1 - x^2 + 7x)\)
`= 3x^5 - 2x^3 + 8x + 9 - 3x^5 + x^4 - 1 + x^2 - 7x`
`= (3x^5 - 3x^5) + x^4 - 2x^3 - x^2 + (8x + 7x) + (9+1)`
`= x^4 - 2x^3 - x^2 + 15x + 10`
\(R( x) = x^4 + 7x^3 - 4 - 4x ( x^2 + 1) + 6x\)
`= x^4 + 7x^3 - 4 - 4x^3 - 4x + 6x`
`= x^4 + (7x^3 - 4x^3) + (-4x + 6x) - 4`
`= x^4 + 3x^3 + 2x - 4`
`@` Tổng:
`H(x)+R(x)=` \((x^4 - 2x^3 - x^2 + 15x + 10)+(x^4 + 3x^3 + 2x - 4)\)
`= x^4 - 2x^3 - x^2 + 15x + 10+x^4 + 3x^3 + 2x - 4`
`= (x^4 + x^4) + (-2x^3 + 3x^3) - x^2 + (15x + 2x) + (10-4)`
`= 2x^4 + x^3 - x^2 + 17x + 6`
`@` Hiệu:
`H(x) - R(x) =`\((x^4 - 2x^3 - x^2 + 15x + 10)-(x^4 + 3x^3 + 2x - 4)\)
`=x^4 - 2x^3 - x^2 + 15x + 10-x^4 - 3x^3 - 2x + 4`
`= (x^4 - x^4) + (-2x^3 - 3x^3) - x^2 + (15x - 2x) + (10+4)`
`= -5x^3 - x^2 + 13x + 14`
`@` `\text {# Kaizuu lv u.}`
![](https://rs.olm.vn/images/avt/0.png?1311)
A(x)=F(x)-G(x)
=1+x+x^2+...+x^100-x^2-x^4-...-x^100
=1+x+x^3+...+x^99
Số số lẻ từ 1 đến 99 là (99-1):2+1=50(số)
A(-1)=1+(-1)+(-1)^3+...+(-1)^99
=1-50*1=1-50=-49
![](https://rs.olm.vn/images/avt/0.png?1311)
`@` `\text {Ans}`
`\downarrow`
*Máy tớ cam hơi mờ, cậu thông cảm ._.*
Cậu viết lại rõ đề câu c, nhé.
Ta có : \(\left(x^2+1\right)\left(x+1\right)=x^3+x^2+x+1\)
\(\left(x+1\right)^2\left(x-1\right)=\left(x^2+2x+1\right)\left(x-1\right)=x^3-x^2+2x^2-2x+x-1\)
\(=x^3-x^2-x-1\)
Ta ko CM đc đẳng thức trên