\(\left(x+3y\right)^4\)
\(=x^4+C^1_4\cdot x^3\cdot3y+C^2_4\cdot x^2\cdot\left(3y\right)^2+C^3_4\cdot x\cdot\left(3y\right)^3+C^4_4\cdot x^0\cdot\left(3y\right)^4\)
\(=x^4+12x^3y+54x^2y^2+108xy^3+81y^4\)
\(\left(2x-5y\right)^5\)
\(=\left(2x\right)^5-C^1_5\cdot\left(2x\right)^4\cdot5y+C^2_5\cdot\left(2x\right)^3\cdot\left(5y\right)^2-C^3_5\cdot\left(2x\right)^2\cdot\left(5y\right)^3+C^4_5\cdot\left(2x\right)^1\cdot\left(5y\right)^4-\left(5y\right)^5\)
\(=32x^5-400x^4y+2000x^3y^2-5000x^2y^3+6250xy^4-3125y^5\)
\(\left(2x+3y\right)^5\)
\(=\left(2x\right)^5+C^1_5\cdot\left(2x\right)^4\cdot3y+C^2_5\cdot\left(2x\right)^3\cdot\left(3y\right)^2+C^3_5\cdot\left(2x\right)^2\cdot\left(3y\right)^3+C^4_5\cdot\left(2x\right)\cdot\left(3y\right)^4+\left(3y\right)^5\)
\(=32x^5+240x^4y+720x^3y^2+1080x^2y^3+810xy^4+243y^5\)
