Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a: \(a\left(x-y\right)-b\left(y-x\right)+c\left(x-y\right)\)
\(=a\left(x-y\right)+b\left(x-y\right)+c\left(x-y\right)\)
\(=\left(x-y\right)\left(a+b+c\right)\)
b: \(a^m-a^{m+2}\)
\(=a^m-a^m\cdot a^2\)
\(=a^m\left(1-a^2\right)\)
\(=a^m\left(1-a\right)\left(1+a\right)\)
\(\left(x+y\right)\left(x^2-y^2\right)+\left(y+z\right)\left(y^2-z^2\right)+\left(z+x\right)\left(z^2-x^2\right)\)
\(=-y^3-xy^2+x^2y+x^3-z^3-yz^2+y^2z+y^3-x^3-zx^2+z^2x+z^3\)
\(=-xy^2+x^2y-yz^2+y^2z-zx^2+z^2x\)
\(=\left(x-y\right)\left(z-x\right)\left(z-y\right)\)
a) \(\left(x+y\right)^5-x-y=\left(x+y\right)^5-\left(x+y\right)=\left(x+y\right)\left[\left(x+y\right)^4-1\right]\)
= \(\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\) #áp dụng hàng đẳng thức#
c) \(x^9-x^7-x^6-x^5+x^4+x^3+x^2+1\)nhóm vào là đc
b) \(\left(x^2+y^2\right)^3+\left(z^2-x^2\right)^3+\left(y^2+z^2\right)^3\)
=\(\left(y^2+x^2\right)\left[\left(x^2+y^2\right)^2-\left(x^2+y^2\right)\left(z^2-x^2\right)+\left(z^2-x^2\right)^2\right]+\left(y^2+z^2\right)^3\)
= \(\left(y^2+z^2\right)\left[x^4+y^4+2x^2y^2-x^2z^2+x^4-y^2z^2+x^2y^2+z^4+x^4-2x^2z^2+y^4+z^4+2y^2z^2\right]\)
=\(=\left(y^2+z^2\right)\left(2x^4+2y^4+2z^4+3x^2y^2-3x^2z^2+y^2z^2\right)\)
nâng cao phát triển toán 8 tập 1 mình ngại viết nên bạn vào đó xem nhé
Mình nghĩ bạn ghi đề sai, đề đúng theo mình là:
\(x^2y^2\left(x-y\right)+y^2z^2\left(y-z\right)+z^2x^2\left(z-x\right)\)
\(=x^2y^2\left(x-y\right)-y^2z^2\text{[}\left(x-y\right)+\left(z-x\right)\text{]}+z^2x^2\left(z-x\right)\)
\(=x^2y^2\left(x-y\right)-y^2z^2\left(x-y\right)-y^2z^2\left(z-x\right)+z^2x^2\left(z-x\right)\)
\(=\left(x-y\right)\left(x^2y^2-y^2z^2\right)+\left(z-x\right)\left(z^2x^2-y^2z^2\right)\)
\(=\left(x-y\right).y^2\left(x+z\right)\left(x-z\right)+\left(z-x\right).z^2\left(x-y\right)\left(x+y\right)\)
\(=\left(x-y\right)\left(x-z\text{ }\right)\text{[}y^2.\left(x+z\right)-z^2\left(x+y\right)\text{]}\)
\(=\left(x-y\right)\left(z-x\right)\left(y^2x+y^2z-z^2x-z^2y\right)\)
\(=\left(x-y\right)\left(z-x\right)\text{[}\left(y^2x-z^2x\right)+\left(y^2z-z^2y\right)\text{]}\)
\(=\left(x-y\right)\left(z-x\right)\text{[}x.\left(y-z\right)\left(y+z\right)+yz\left(y-z\right)\text{]}\)
\(=\left(x-y\right)\left(x-z\right)\left(y-z\right)\left(xy+x\text{z}+yz\right)\)
a) xy(x + y) + yz(y + z) + xz(z + x) + 3xyz
= xy(X + y + z) + yz(x + y + z) + xz(X + y + z)
= (x + y +z)(xy + yz+ xz)
b) xy(x + y) - yz(y + z) - xz(z - x)
= x2y + xy2 - y2z - yz2 - xz2 + x2z
= x2(y + z) - yz(y + z) + x(y2 - z2)
= x2(y + z) - yz(y + z) + x(y + z)(y - z)
= (y + z)(x2 - yz + xy - xz)
= (y + z)[x(x + y) - z(x + y)]
= (y + z)(x + y)(x - z)
c) x(y2 - z2) + y(z2 - x2) + z(x2 - y2)
= x(y - z)(y + z) + yz2 - yx2 + x2z - y2z
= x(y - z)(y + z) - yz(y - z) - x2(y - z)
= (y - z)((xy + xz - yz - x2)
= (y - z)[x(y - x) - z(y - x)]
= (y - z)(x - z)(y -x)
a) \(2\left(x+y\right)^2-7\left(x+y\right)+5\)
\(=2\left(x+y\right)^2-2\left(x+y\right)-5\left(x+y\right)+5\)
\(=2\left(x+y\right)\left(x+y-1\right)-5\left(x+y-1\right)\)
\(=\left(x+y-1\right)\left(2x+2y-5\right)\)
b) c) tương tự