Rút gọn cái biểu thức sau:
A= 4,9.15+15.3,7-4,9.5+3,7.85
B= x15 - 8x14 + 8x13 - 8x12 + ... - 8x2 + 8x - 5. Khi x=7
C= 2y-x- { 2x-y-[ y+32-(5y-x) ] }. Khi x= a2 + 2ab+b2 ; y= a2 - 2ab + b2
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`B = x^15 - 8x^14 + 8x^13 - 8x^122 + ... - 8x^2 + 8x - 5`
`B = x^15 - 7x^14 -x^14+7x^13+x^13-7x^12-...-x^2+7x+x-5`
`B = x^14(x-7) - x^14(x-7) +...+x^2(x-7)-x(x-7)+x-5`
`B = 7-5=2`
x=7 nên x+1=8
\(B=x^{15}-x^{14}\left(x+1\right)+x^{13}\left(x+1\right)-x^{12}\left(x+1\right)+...-x^2\left(x+1\right)+x\left(x+1\right)-5\)
\(=x^{15}-x^{15}-x^{14}+x^{14}-x^{13}+x^{13}-...-x^3-x^2+x^2+x+5\)
=x+5
=7+5
=12
B = x15 - 8x14 + 8x13 - 8x2 + ... - 8x2 + 8x - 5
B = x^15 - 7x^14 -x^14+7x^13+x^13-7x^12-...-x^2+7x+x-5
B = x^14(x-7) - x^14(x-7) +...+x^2(x-7)-x(x-7)+x-5
B = 7-5=2
`B = x^15 - 7x^14 - x^14 + 7x^13 + x^13 - .... +7x + x - 7 + 2`
`<=> x^14(x-7) - x^13(x-7) + ... + x - 7 + 2`
`<=> (x^14-x^13 + ... + 1)(x-7) + 2`
Thay `x = 7 <=> (x^14 - x^13 + ... + 1) xx 0 + 2 = 2`.
ta có: 8=7+1=x+1
\(B=x^{15}-8x^{14}+8x^{13}-...-8x^2+8x-5\)
\(\Rightarrow B=x^{15}-\left(x+1\right)x^{14}+\left(x+1\right)x^{13}-...-\left(x+1\right)x^2+\left(x+1\right)x-5\)
\(\Rightarrow B=x^{15}-x^{15}-x^{14}+x^{14}+x^{13}-...-x^3-x^2+x^2+x-5\)
\(\Rightarrow B=x-5\)
\(\Rightarrow B=7-5\)
\(\Rightarrow B=2\)
\(B=x^{15}-8x^{14}+8x^{13}-8x^{12}+...+8x-5\)
\(=x^{15}-\left(x+1\right)x^{14}+\left(x+1\right)x^{13}-\left(x+1\right)x^{12}+...+\left(x+1\right)x-x+2\)
\(=x^{15}-x^{15}-x^{14}+x^{14}+x^{13}-x^{13}-x^{12}+...+x^2+x-x+2\)
\(=2\)