Question

7 cau 7 like

Answer 1

a: \(\frac13x^2y^5\cdot\left(-\frac35x^3y\right)+x^5y^6\)

\(=\left(\frac13\cdot\frac{-3}{5}\right)\cdot x^2\cdot x^3\cdot y^5\cdot y+x^5y^6\)

\(=-\frac15x^5y^6+x^5y^6=\frac45x^5y^6\)

b: \(5xy^2\left(-\frac{3}{10}x^2y\right)+\frac34x^3y^3\)

\(=5\cdot\left(-\frac{3}{10}\right)\cdot x\cdot x^2\cdot y^2\cdot y+\frac34x^3y^3\)

\(=-\frac32x^3y^3+\frac34x^3y^3=-\frac34x^3y^3\)

c: \(\frac14x^4y\left(-\frac23x^3y^2\right)-\frac13x^7y^3\)

\(=\left(\frac14\cdot\frac{-2}{3}\right)\cdot x^4\cdot x^3\cdot y\cdot y^2-\frac13x^7y^3\)

\(=-\frac16x^7y^3-\frac13x^7y^3=-\frac12x^7y^3\)

d: \(\frac17x^2y^3\cdot\left(-\frac{14}{3}xy^2\right)-\frac12xy\cdot x^2y^4\)

\(=\left(\frac17\cdot\frac{-14}{3}\right)\cdot x^2\cdot x\cdot y^3\cdot y^2-\frac12x^3y^5\)

\(=-\frac23x^3y^5-\frac12x^3y^5=-\frac76x^3y^5\)

e: \(\frac25x^4y^5\cdot\left(\frac54x^2y^3\right)+\frac53x^2y^3\cdot\left(-\frac{9}{10}x^4y^5\right)\)

\(=\frac25\cdot\frac54\cdot x^4y^5\cdot x^2y^3+\frac53\cdot\frac{-9}{10}\cdot x^2y^3\cdot x^4y^5\)

\(=\frac12x^6y^8+\frac{-3}{2}x^6y^8=-x^6y^8\)

f: \(\frac12xy^2\left(-\frac23x^2y\right)^2-5xy\cdot\left(-\frac12x^4y^3\right)+\left(-\frac12x^2y\right)^2\cdot xy^2\)

\(=\frac12xy^2\cdot\frac49x^4y^2+\frac52x^5y^4+\frac14x^4y^2\cdot xy^2\)

\(=\frac29x^5y^4+\frac52x^5y^4+\frac14x^5y^4=x^5y^4\left(\frac29+\frac52+\frac14\right)\)

\(=x^5y^4\left(\frac{8}{36}+\frac{90}{36}+\frac{9}{36}\right)=x^5y^4\cdot\frac{107}{36}\)

g: \(-\frac52\left(xy\right)^2\cdot x^3+\frac37\cdot\left(2x\right)^3\cdot\left(\frac72xy\right)^2-\frac13x\cdot3x^4y^2\)

\(=-\frac52x^3\cdot x^2y^2+\frac37\cdot8x^3\cdot\frac{49}{4}x^2y^2-x^5y^2\)

\(=-\frac52x^5y^2+42x^5y^2-x^5y^2=38,5x^5y^2\)