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Làm trc cho 2 câu cuối
c) \(a^2-b^2-4a+4b\)
\(=\left(a+b\right)\left(a-b\right)-4\left(a-b\right)\)
\(=\left(a-b\right)\left[\left(a+b\right)-4\right]\)
d) \(a^2+2ab+b^2-2a-2b+1\)
\(=\left(a+b\right)^2-2\left(a+b\right)+1\)
\(=\left(a+b\right)\left[\left(a+b\right)-2\right]+1\)
\(201^2=\left(200+1\right)^2=200^2+2.200.1+1^2=40000+400+1=40401\)
\(498^2=\left(500-2\right)^2=500^2-2.500.2+2^2=250000-2000+4=248004\)
Nhớ ghi dấu ngoặc tránh giải sai.
\(a.\) \(\frac{x+4}{2x+6}+\frac{3}{x^2-9}\)
Ta có:
\(2x+6=2\left(x+3\right)\)
\(x^2-9=\left(x-3\right)\left(x+3\right)\)
nên \(MTC:\) \(2\left(x-3\right)\left(x+3\right)\)
Do đó: \(\frac{x+4}{2x+6}+\frac{3}{x^2-9}=\frac{x+4}{2\left(x+3\right)}+\frac{3}{\left(x-3\right)\left(x+3\right)}=\frac{\left(x+4\right)\left(x-3\right)}{2\left(x-3\right)\left(x+3\right)}+\frac{2.3}{2\left(x-3\right)\left(x+3\right)}=\frac{x^2+x-12+6}{2\left(x-3\right)\left(x+3\right)}\)
\(=\frac{x^2+x-6}{2\left(x-3\right)\left(x+3\right)}=\frac{x^2-2x+3x-6}{2\left(x-3\right)\left(x+3\right)}=\frac{x\left(x-2\right)+3\left(x-2\right)}{2\left(x-3\right)\left(x+3\right)}=\frac{\left(x-2\right)\left(x+3\right)}{2\left(x-3\right)\left(x+3\right)}=\frac{x-2}{2\left(x-3\right)}\)
câu b nè
\(\frac{3x+1}{\left(x-1\right)^2}-\frac{1}{x+1}-\frac{x+3}{x^2-1}\)
=\(\frac{\left(3x+1\right)\left(x+1\right)}{\left(x-1\right)^2\left(x+1\right)}-\frac{\left(x-1\right)^2}{\left(x-1\right)^2\left(x+1\right)}-\frac{\left(x+3\right)\left(x-1\right)}{\left(x-1\right)^2\left(x+1\right)}\)
=\(\frac{\left(3x^2+x+3x+1\right)-\left(x^2-2x+1\right)-\left(x^2-x-3+3x\right)}{\left(x-1\right)^2\left(x+1\right)}\)
=\(\frac{3x^2+4x+1-x^2+2x-1-x^2-2x+3}{\left(x-1\right)^2\left(x+1\right)}=\frac{x^2+4x+3}{\left(x+1\right)\left(x-1^2\right)}\)
=\(\frac{\left(x+1\right)\left(x+3\right)}{\left(x+1\right)\left(x-1\right)^2}=\frac{x+3}{\left(x-1\right)^2}\)
đơn giản
nhưng trả lời câu hỏi của tớ đã
\(x^3+8x^2+17x+10\)
\(=x^3+2x^2+x^2+5x^2+10x+5x+2x+10\)
\(=\left(x^3+x^2\right)+\left(2x^2+2x\right)+\left(5x^2+5x\right)+\left(10x+10\right)\)
\(=x^2\left(x+1\right)+2x\left(x+1\right)+5x\left(x+1\right)+10\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+2x+5x+10\right)\)
\(=\left(x+1\right)\left[x\left(x+2\right)+5\left(x+2\right)\right]\)
\(=\left(x+1\right)\left(x+2\right)\left(x+5\right)\)
a, 2015^2 - 2014^2
=(2015-2014)(2015+2014)
=1.4029
=4029
b, 1^2 - 2^2 + 3^2 - 4^2 + ......+ 99^2 - 100^2
=(1-2)(1+2)+(3-4)(3+4)+...+(99-100)(99+100)
=-(1+2)-(3+4)-...-(99+100)
=-1-2-3-4-...-99-100
=(-1-100).100:2=-5050