Step-by-step explanation:
is the same as
[tex]x^5 + 3^5\\x^5 + 243[/tex]
Does that make sense
please mark brainest
Given expression :
[tex]{\qquad \sf \dashrightarrow{ (x+3)^{5} } }[/tex]
We need to simplify it.
We can write the expression as,
[tex]{\qquad \sf \dashrightarrow{ (x+3)^{} }{ (x+3)^{} }{ (x+3)^{} }{ (x+3)^{} }{ (x+3)^{} }}[/tex]
[tex]{\qquad \sf \dashrightarrow{ (x+3)^{2} }{ (x+3)^{2} }{ (x+3)^{} }}[/tex]
We know that,
[tex]{\qquad \sf \dashrightarrow{ (a+b)^{2} } = {a}^{2} + 2ab + {b}^{2} }[/tex]
Now, using the formula in the expression:
[tex]{\qquad \sf \dashrightarrow{ (x {}^{2} + 2x.3 +3^{2}) }{ (x {}^{2} + 2x.3 +3^{2}) }{ (x+3)^{} }}[/tex]
[tex]{\qquad \sf \dashrightarrow{ (x {}^{2} + 6x +9) }{ (x {}^{2} + 6x +9) }{ (x+3)^{} }}[/tex]
[tex]{\qquad \sf \dashrightarrow{ ( {x}^{4} + 6 {x}^{3} + 9 {x }^{2} + 6x {}^{3} + 36 {x}^{2} + 54x + 9 {x}^{2} + 54x + 81 ) }{ (x+3)^{} }}[/tex]
[tex]{\qquad \sf \dashrightarrow{ ( {x}^{4} + 12{x}^{3} + 54 {x }^{2} + 108x + 81 ) }{ (x+3)^{} }}[/tex]
[tex]{\qquad \sf \dashrightarrow{ \: {x}^{5} + 12 {x}^{4} + 54 {x}^{3} + 108 {x}^{2} + 81x + 3 {x}^{4} + 36x {}^{3} + 162 {x}^{2} + 324x + 243 }}[/tex]
Adding the like terms we get :
[tex]{\qquad \sf \dashrightarrow{ \: {x}^{5} + 15 {x}^{4} + 90 {x}^{3} + 270 {x}^{2} + 405x + 243 }}[/tex]
