Mọi người giúp mình nha????
Bài 1:thu gọn đa thức
a,\(-\frac{1}{3}xy\cdot\left(3x^2yz^2\right)\)
b,\(-54y^2\cdot bx\) với b là hằng số
c,\(-2x^2y\cdot\left(\frac{1}{2}\right)^2\cdot x\cdot\left(y^2x\right)^3\)
Bài 2:cho 2 đa thức:
\(f\left(x\right)=x^5-3x^2+7x^4-9x^3-\frac{1}{4}\)
\(g\left(x\right)=5x^4-x^5+x^2+3x^2-\frac{1}{4}\)
a,Hãy thu gọn và sắp xếp hai đa thức trên
b,Tính \(f\left(x\right)+g\left(x\right)\) và \(f\left(x\right)-g\left(x\right)\)
Bài 3:Cho \(f\left(x\right)=-15x^2+5x^4-4x^2+8x^2-9x^3-x^4+15-7x^3\)
a,Thu gọn f(x)
b,Tính f(1) và f(-1)
bài 1
a) \(-\frac{1}{3}xy\).(3\(x^2yz^2\))
=\(\left(-\frac{1}{3}.3\right)\).\(\left(x.x^2\right)\).(y.y).\(z^2\)
=\(-x^3\).\(y^2z^2\)
b)-54\(y^2\).b.x
=(-54.b).\(y^2x\)
=-54b\(y^2x\)
c) -2.\(x^2y.\left(\frac{1}{2}\right)^2.x.\left(y^2.x\right)^3\)
=\(-2x^2y.\frac{1}{4}.x.y^6.x^3\)
=\(\left(-2.\frac{1}{4}\right).\left(x^2.x.x^3\right).\left(y.y^2\right)\)
=\(\frac{-1}{2}x^6y^3\)
Bài 3:
a) \(f\left(x\right)=-15x^2+5x^4-4x^2+8x^2-9x^3-x^4+15-7x^3\)
\(f\left(x\right)=\left(5x^4-x^4\right)-\left(9x^3+7x^3\right)-\left(15x^2+4x^2-8x^2\right)+15\)
\(f\left(x\right)=4x^4-16x^3-11x^2+15\)
b)
\(f\left(x\right)=4x^4-16x^3-11x^2+15\)
\(f\left(1\right)=4\cdot1^4-16\cdot1^3-11\cdot1^2+15\)
\(f\left(1\right)=4\cdot1^4-16\cdot1^3-11\cdot1^2+15\)
\(f\left(1\right)=-8\)
\(f\left(x\right)=4x^4-16x^3-11x^2+15\)
\(f\left(-1\right)=4\cdot\left(-1\right)^4-16\cdot\left(-1\right)^3-11\cdot\left(-1\right)^2+15\)
\(f\left(-1\right)=24\)
Bài 1:
a) \(-\frac{1}{3}xy\cdot\left(3x^2yz^2\right)\)
\(=\left(-\frac{1}{3}\cdot3\right)\left(xx^2\right)\left(yy\right)z\)
\(=-x^3y^2z\)
b) \(-54y^2\cdot bx\)
\(=\left(-54b\right)xy^2\)
c) \(-2x^2y\cdot\left(\frac{1}{2}\right)^2\cdot x\cdot\left(y^2x\right)^3\)
\(=-2x^2y\cdot\frac{1}{4}\cdot x\cdot y^5x^3\)
\(=\left(-2\cdot\frac{1}{4}\right)\left(x^2xx^3\right)\left(yy^5\right)\)
\(=-\frac{1}{2}x^6y^6\)
Bài 2:
a) \(f\left(x\right)=x^5-3x^2+7x^4-9x^3-\frac{1}{4}\)
\(f\left(x\right)=x^5+7x^4-9x^3-3x^2-\frac{1}{4}\)
\(g\left(x\right)=5x^4-x^5+x^2+3x^2-\frac{1}{4}\)
\(g\left(x\right)=-x^5+5x^4+\left(x^2+3x^2\right)-\frac{1}{4}\)
\(g\left(x\right)=-x^5+5x^4+4x^2-\frac{1}{4}\)
b) \(f\left(x\right)+g\left(x\right)=\left(x^5+7x^4-9x^3-3x^2-\frac{1}{4}\right)+\left(-x^5+5x^4+4x^2-\frac{1}{4}\right)\)
\(f\left(x\right)+g\left(x\right)=x^5+7x^4-9x^3-3x^2-\frac{1}{4}-x^5+5x^4+4x^2-\frac{1}{4}\)
\(f\left(x\right)+g\left(x\right)=\left(x^5-x^5\right)+\left(7x^4+5x^4\right)-9x^3+\left(-3x^2+4x^2\right)-\left(\frac{1}{4}+\frac{1}{4}\right)\)
\(f\left(x\right)+g\left(x\right)=12x^4-9x^3+x^2-\frac{1}{2}\)
\(f\left(x\right)-g\left(x\right)=\left(x^5+7x^4-9x^3-3x^2-\frac{1}{4}\right)-\left(-x^5+5x^4+4x^2-\frac{1}{4}\right)\)
\(f\left(x\right)-g\left(x\right)=x^5+7x^4-9x^3-3x^2-\frac{1}{4}+x^5-5x^4-4x^2+\frac{1}{4}\)
\(f\left(x\right)-g\left(x\right)=\left(x^5+x^5\right)+\left(7x^4-5x^4\right)-9x^3-\left(3x^2+4x^2\right)+\left(-\frac{1}{4}+\frac{1}{4}\right)\)
\(f\left(x\right)-g\left(x\right)=2x^5+2x^4-9x^3-7x^2\)