2A +3 = 3 mũ4n+1
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1:
a: \(\left(x+y+z\right)^2=x^2+y^2+z^2+2xy+2zx+2yz\)
b: \(\left(x-y+z\right)^2=x^2+y^2+z^2-2xy+2xz-2yz\)
c: \(\left(x-y-z\right)^2=x^2+y^2+z^2-2xy-2xz+2yz\)
a) A=(4-5x)2-(3+5x)2=(4-5x-3-5x)(4-5x+3+5x)=(-25x+1)1=-25x+1
B=(3x-1)(1+3x)-(3x+1)2=9x2-1-(3x+1)2=9x2-1-(9x2+6x+1)=9x2-1-9x2-6x-1=-6x-2=-2(3x+1)
cái này trong toán violympic tiếng anh cấp tỉnh vong 9 do
\(a)\) \(\left(\frac{1}{2}a+b\right)^3+\left(\frac{1}{2}a-b\right)^3\)
\(=\)\(\left(\frac{1}{2}a+b+\frac{1}{2}a-b\right)\left[\left(\frac{1}{2}a+b\right)^2-\left(\frac{1}{2}a+b\right)\left(\frac{1}{2}a-b\right)+\left(\frac{1}{2}a-b\right)^2\right]\)
\(=\)\(a\left[\left(\frac{1}{2}a\right)^2+2\frac{1}{2}ab+b^2-\left(\frac{1}{2}a\right)^2+b^2+\left(\frac{1}{2}a\right)^2-2.\frac{1}{2}ab+b^2\right]\)
\(=\)\(a\left(\frac{1}{4}a^2+ab+b^2-\frac{1}{4}a^2+b^2+\frac{1}{4}a^2-ab+b^2\right)\)
\(=\)\(a\left(\frac{1}{4}a^2+3b^2\right)\)
\(=\)\(\frac{1}{4}a^3+3b^2\)
Chúc bạn học tốt ~
ĐKXĐ: \(a\ne\pm\frac{1}{2}\)
\(\left(\frac{2a-1}{2a+1}-\frac{2a-3}{2a-1}\right):\frac{2a-1}{2a+1}\)
\(=\left(\frac{\left(2a-1\right)^2}{\left(2a+1\right)\left(2a-1\right)}-\frac{\left(2a-3\right)\left(2a+1\right)}{\left(2a-1\right)\left(2a+1\right)}\right).\frac{2a+1}{2a-1}\)
\(=\left(\frac{4a^2-4a+1}{\left(2a+1\right)\left(2a-1\right)}-\frac{4a^2-4a+3}{\left(2a+1\right)\left(2a-1\right)}\right).\frac{2a+1}{2a-1}\)
\(=\frac{-2}{\left(2a+1\right)\left(2a-1\right)}.\frac{2a+1}{2a-1}=\frac{-2}{\left(2a-1\right)^2}\)