Answer :
[5y]³+[4z]³
by using identity a³+b³=a³+b³+3a²b+3ab²
[5y]³+[4z]³+3×[5y]²×[4z]+3×[5y]×[4z]²
125y³+64z³+225y²z+240yz²
by using identity a³+b³=a³+b³+3a²b+3ab²
[5y]³+[4z]³+3×[5y]²×[4z]+3×[5y]×[4z]²
125y³+64z³+225y²z+240yz²
[tex]125y^3 + 64z^3 [/tex]
[tex]= (5y)^3 + (4z)^3 [/tex]
[tex]Using\ identity:\ a^3+b^3=(a+b)(a^2+b^2-ab)[/tex]
We have: [tex](5y+4z)[(5y)^2+(4z)^2-(5y)(4z)][/tex]
[tex]=(5y+4z)(25y^2+16z^2-40yz)[/tex]
[tex]= (5y)^3 + (4z)^3 [/tex]
[tex]Using\ identity:\ a^3+b^3=(a+b)(a^2+b^2-ab)[/tex]
We have: [tex](5y+4z)[(5y)^2+(4z)^2-(5y)(4z)][/tex]
[tex]=(5y+4z)(25y^2+16z^2-40yz)[/tex]