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a)
\(P=\left(x^{14}-9x^{13}\right)-\left(x^{13}-9x^{12}\right)+\left(x^{12}-9x^{11}\right)-...+\left(x^2-9x\right)-\left(x-9\right)+1\)
\(=x^{13}\left(x-9\right)-x^{12}\left(x-9\right)+x^{11}\left(x-9\right)+...+x\left(x-9\right)-\left(x-9\right)+1\)
\(P\left(9\right)=1\)
b)
\(Q=\left(x^{15}-7x^{14}\right)-\left(x^{14}-7x^{13}\right)+\left(x^{13}-7x^{12}\right)-...-\left(x^2-7x\right)+\left(x-7\right)+2\)
\(=x^{14}\left(x-7\right)-x^{13}\left(x-7\right)+x^{12}\left(x-7\right)-...-x\left(x-7\right)+\left(x-7\right)+2\)
\(Q\left(7\right)=2\)
\(A=2y-x-\left\{2x-y-\left[y+3x-\left(5y-x\right)\right]\right\}\)
\(=2y-x-\left\{2x-y-\left[y+3x-5y+x\right]\right\}\)
\(=2y-x-\left\{2x-y-y-3x+5y-x\right\}\)
\(=2y-x-2x+y+y+3x-5y+x\)
\(=\left(2y+y+y-5y\right)+\left(-x-2x+3x+x\right)\)
= \(-y+x\)
Thay \(x=a^2+2ab+b^2,y=a^2-2ab+b^2\) vào đa thức -y + x :
\(-\left(a^2-2ab+b^2\right)+\left(a^2+2ab+b^2\right)\)
\(=-a^2+2ab-b^2+a^2+2ab+b^2\)
\(=\left(-a^2+a^2\right)+\left(2ab+2ab\right)+\left(-b^2+b^2\right)\)
= 4ab
\(A=2y-x-\left\{2x-y-\left[y+3x-\left(5y-x\right)\right]\right\}\\ =2y-x-\left\{2x-y-y-3x+5y-x\right\}\\ =2y-x-2x+y+y+3x-5y+x\\ =-y+x=-\left(a^2-2ab+b^2\right)+\left(a^2+2ab+b^2\right)\\ =-a^2+2ab-b^2+a^2+2ab+b^2=4ab\)
Biểu thức x ( a 2 - a b + b 2 + y ) có các biến là x, y
Chọn đáp án C
a: M+N-P
\(=7a^2-2a+1-a^2+4\)
\(=6a^2-2a+5\)
b: \(=2y-x-2x+y+y+3x-5y+x\)
\(=-3x+3y-4y+4x=x-y\)
\(=a^2+2ab+b^2-a^2+2ab-b^2=4ab\)
c: \(=\left[{}\begin{matrix}5x-3-2x+1=3x-2\left(x>=\dfrac{1}{2}\right)\\5x-3+2x-1=7x-4\left(x< \dfrac{1}{2}\right)\end{matrix}\right.\)
\(B=x^{15}-8x^{14}+8x^{13}-8x^{12}+...+8x-5\)
\(=x^{15}-\left(x+1\right)x^{14}+\left(x+1\right)x^{13}-\left(x+1\right)x^{12}+...+\left(x+1\right)x-x+2\)
\(=x^{15}-x^{15}-x^{14}+x^{14}+x^{13}-x^{13}-x^{12}+...+x^2+x-x+2\)
\(=2\)