Bài 1 Thu gọn:
a, (a+2)3 -a.(a-3)2
Bài 2 Tính nhẩm:
262+52.24+242
Các bạn giúp mk nha. THANKS
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b) Ta có
A = 3 + 32 + ... + 32004.a)A=3+32+33+...+32004
=>3A=32+33+34+...+32005
=>3A-A=(32+33+34+...+32005)-(3+32+33+...+32004)
=>2A=32+33+34+...+32005-3-32-33-...-32004
=>2A=32005-3
=>A=32005−32
1, gọ̣̣i bthứ́c trên là A, ta có:
A=8y3-12y2+6y-1-2y*(4y2-12y+9)-12y2+12y
A=8y3-12y2+6y-1-8y3+24y2-18y-12y2+12y
A=-1
vây bthức A ko phu thuôc vào biến y
Bài 3:
a: \(\frac{x}{x-3}+\frac{9-6x}{x^2-3x}\)
\(=\frac{x}{x-3}+\frac{-6x+9}{x\left(x-3\right)}\)
\(=\frac{x^2-6x+9}{x\left(x-3\right)}=\frac{\left(x-3\right)^2}{x\left(x-3\right)}=\frac{x-3}{x}\)
b: \(\frac{6x-3}{x}:\frac{4x^2-1}{3x^2}\)
\(=\frac{3\left(2x-1\right)}{x}\cdot\frac{3x^2}{\left(2x-1\right)\left(2x+1\right)}=\frac{3\cdot3x}{2x+1}=\frac{9x}{2x+1}\)
Bài 2:
a: \(\frac{x^3-x}{3x+3}\)
\(=\frac{x\left(x^2-1\right)}{3\left(x+1\right)}=\frac{x\left(x-1\right)\left(x+1\right)}{3\left(x+1\right)}=\frac{x\left(x-1\right)}{3}\)
b: \(\frac{x^2+3xy}{x^2-9y^2}=\frac{x\left(x+3y\right)}{\left(x-3y\right)\left(x+3y\right)}=\frac{x}{x-3y}\)
Bài 1:
a: \(\frac{x^2-9}{2x+6}:\frac{3-x}{2}\)
\(=\frac{\left(x-3\right)\left(x+3\right)}{2\left(x+3\right)}\cdot\frac{2}{-\left(x-3\right)}=\frac{-2}{2}=-1\)
b: \(\frac{2x}{x-y}-\frac{2y}{x-y}=\frac{2x-2y}{x-y}=\frac{2\left(x-y\right)}{x-y}=2\)
c: \(\frac{x+15}{x^2-9}+\frac{2}{x+3}\)
\(=\frac{x+15}{\left(x-3\right)\left(x+3\right)}+\frac{2}{x+3}\)
\(=\frac{x+15+2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}=\frac{x+15+2x-6}{\left(x-3\right)\left(x+3\right)}=\frac{3x+9}{\left(x-3\right)\left(x+3\right)}\)
\(=\frac{3\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\frac{3}{x-3}\)
d: \(\frac{x+y}{2x-2y}-\frac{x-y}{2x+2y}-\frac{y^2+x^2}{y^2-x^2}\)
\(=\frac{x+y}{2\left(x-y\right)}-\frac{x-y}{2\left(x+y\right)}+\frac{x^2+y^2}{\left(x-y\right)\left(x+y\right)}\)
\(=\frac{\left(x+y\right)^2-\left(x-y\right)^2+2\left(x^2+y^2\right)}{2\left(x-y\right)\left(x+y\right)}=\frac{x^2+2xy+y^2-x^2+2xy-y^2+2x^2+2y^2}{2\left(x-y\right)\left(x+y\right)}\)
\(=\frac{2x^2+4xy+2y^2}{2\left(x-y\right)\left(x+y\right)}=\frac{2\left(x^2+2xy+y^2\right)}{2\left(x-y\right)\left(x+y\right)}=\frac{\left(x+y\right)^2}{\left(x-y\right)\left(x+y\right)}=\frac{x+y}{x-y}\)
a) \(\left(x-3\right)^2.\left(x+3\right).\left(x-3\right)\)
\(=\left(x-3\right).\left(x-3\right).\left(x+3\right).\left(x-3\right)\)
\(=\left(x-3\right)^3.\left(x+3\right)\)
\(=\left(3x-9\right).\left(x+3\right)\)
Phần b tương tự