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xn - 1(x + y) - y(xn - 1 + yn - 1)
= xn - x + y - yxn - y2 n - 1
x(x – y) + y(x – y)
= x.x – x.y + y.x – y.y
= x2 – xy + xy – y2
= x2 – y2 + (xy – xy)
= x2 – y2
a: ta có: \(x\left(x-y\right)+y\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y\right)\)
\(=x^2-y^2\)
b: Ta có: \(x^{n-1}\left(x+y\right)-y\left(x^{n-1}+y^{n-1}\right)\)
\(=x^n+x^{n-1}\cdot y-x^{n-1}\cdot y-y^n\)
\(=x^n-y^n\)
\(x^{n-1}\left(x+y\right)-y\left(x^{n-1}+y^{n-1}\right)\)
=\(x^n+x^{n-1}y-x^{n-1}y-y^n\)
=\(x^n-y^n\)
\(x\left(x-y\right)+y\left(x-y\right)\)
\(=x.x-x.y+y.x-y.y\)
\(=x^2-xy+yx-y^2\)
=\(x^2-y^2\)
a) x(x – y) + y(x – y) = x2 – xy + yx – y2 = x2 – xy + xy – y2 = x2 – y2
b) xn–1(x + y) – y( xn–1 + yn–1 ) = xn + xn–1y – yxn–1 – yn
= xn + xn–1y – xn–1y – yn = xn - yn
a) x (x - y) + y (x - y) = x2 – xy+ yx – y2
= x2 – xy+ xy – y2
= x2 – y2
b) xn – 1 (x + y) – y(xn – 1 + yn – 1) =xn+ xn – 1y – yxn – 1 - yn
= xn + xn – 1y - xn – 1y - yn
= xn – yn.
a. x4 : xn = x4 - n
b. xn : x5 = xn - 5
c. \(\left(3x^4y^3+\dfrac{1}{2}x^3y^2+x^5y\right):4x^ny^n\)
= \(3x^4y^3:4x^ny^n+\dfrac{1}{2}x^3y^2:4x^ny^n+x^5y:4x^ny^n\)
= \(\dfrac{3}{4}x^{4-n}y^{3-n}+\dfrac{1}{8}x^{3-n}y^{2-n}+\dfrac{1}{4}x^{5-n}y^{1-n}\)