1) \(=3a^2b-a^2b+2a^2b+6a^2b=\left(3-1+2+6\right)a^2b=10a^2b\)
2) \(=-4,2a^2-0,3a^2+0,5a^2+3a^2=\left(-4,2-0,3+0,5+3\right)a^2=-a^2\)
3) \(=15x^4+7x^4-20x^2x^2=15x^4+7x^4-20x^4=\left(15+7-20\right)x^4=2x^4\)
4) \(=23x^3y^3+17x^3y^3-50x^3y^3=\left(23+17-50\right)x^3y^3=-10x^3y^3\)
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Tính
a) \(3a^2b+\left(-3a^2b\right)+2a^2b-\left(-6a^2b\right)\)
b)\(\left(-4,2.f^2\right)+\left(-0,3.p^2\right)+0,5.p^2+3.p^2\)
Tính
a) \(3a^2b+\left(-3a^2b\right)+2a^2b-\left(-b.a^2b\right)\)
b)\(\left(-4,2.p^2\right)+\left(-0,3.p^2\right)+0,5.p^2+3.p^2\)
Chứng minh rằng:\(\left(a^3+b^3\right)^2-\left(2a^2b+2b^2a\right)^2=a^6-b^6\)
Chứng minh rằng nếu:
\(\frac{a^4+b^4}{b^4+c^4}=\frac{2a^2b^2}{2b^2c^2}=\frac{4\left(a^2b^2+a^3.b+b^3.a\right)}{4\left(b^2c^2+b^3.c+c^3.b\right)}\)
thì\(b^2=ca\)
Cho \(f\left(x\right)=ax^2+bx+c\) (a ,b,c là các số thực )
a) Biết 10a+2b-5c=0 . Chứng minh\(f\left(-1\right).f\left(-4\right)\ge0\)
b) Biết 13a + b + 2c=0 . Chứng minh \(f\left(-2\right).f\left(3\right)\le0\)
Cho \(\left(a+b\right)\left(2b-a-4\right)=\left(a-2b\right)\left(5-a-b\right)\). Tính \(\frac{2a^2-3b^2}{ab+b^2}\)
Tính tổng:
a/ \(\left(-5x^2y+3xy^2+7\right)+\left(-6x^2y+4xy^2-5\right)\)
b/ \(\left(2,4a^3-10a^2b\right)+\left(7a^2b-2,4a^3+3ab^2\right)\)
c/ \(\left(15x^2y-7xy^2-6y^3\right)+\left(2x^3-12x^2y+7xy^2\right)\)
Cho \(\frac{a}{b}=\frac{c}{d}\). Chứng minh:
a) \(\frac{\left(a-b\right)^3}{\left(c-d\right)^3}=\frac{3a^2+2b^2}{3c^2+2d^2}\)
b)\(\frac{4a^4+5b^4}{4c^4+5d^4}=\frac{a^2b^2}{c^2d^2}\)
c)\(\left(\frac{a-b}{c-d}\right)^{2005}=\frac{2a^{2005}-b^{2005}}{2c^{2005}-d^{2005}}\)
d)\(\frac{2a^{2005}+5b^{2005}}{2c^{2005}+5d^{2005}}=\frac{\left(a+b\right)^{2005}}{\left(c+d\right)^{2005}}\)
e)\(\frac{\left(20a^{2006}+11b^{2006}\right)^{2007}}{\left(20a^{2007}-11b^{2007}\right)^{2006}}=\frac{\left(20c^{2006}+11d^{2006}\right)^{2007}}{\left(20c^{2007}-11d^{2007}\right)^{2006}}\)
f)\(\frac{\left(20a^{2007}-11c^{2007}\right)^{2006}}{\left(20a^{2006}+11c^{2006}\right)^{2007}}=\frac{\left(20b^{2007}-11d^{2007}\right)^{2006}}{\left(20b^{2006}+11d^{2006}\right)^{2007}}\)
Tính:
\(a)\left(-2x^2\right)\cdot\left(3x-4x^3+7-x^2\right)\)
\(b)\left(x+3\right)\cdot\left(2x^2-3x-5\right)\)
\(c)\left(-6x^5+7x^4-6x^3\right):3x^3\)
\(d)\left(9x^2-4\right):\left(3x+2\right)\)
\(e)\left(2x^4-13x^3+15x^2+11x-3\right):\left(x^2-4x-3\right)\)
