Answer:
[tex]\mathrm{Expand}\:\left(x^{10}+10y^{12}\right)^2:\quad x^{20}+20x^{10}y^{12}+100y^{24}[/tex]
Step-by-step explanation:
[tex]\left(x^{10}+10y^{12}\right)^2[/tex]
[tex]\gray{\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2}[/tex]
[tex]\gray{a=x^{10},\:\:b=10y^{12}}[/tex]
[tex]=\left(x^{10}\right)^2+2x^{10}\cdot \:10y^{12}+\left(10y^{12}\right)^2[/tex]
[tex]\black{\mathrm{Simplify}\:\left(x^{10}\right)^2+2x^{10}\cdot \:10y^{12}+\left(10y^{12}\right)^2:}[/tex]
[tex]\left(x^{10}\right)^2+2x^{10}\cdot \:10y^{12}+\left(10y^{12}\right)^2[/tex]
[tex]\gray{\left(x^{10}\right)^2=x^{20}}[/tex]
[tex]\gray{2x^{10}\cdot \:10y^{12}=20x^{10}y^{12}}[/tex]
[tex]\gray{\left(10y^{12}\right)^2=100y^{24}}[/tex]
[tex]=x^{20}+20x^{10}y^{12}+100y^{24}[/tex]
