Question

Please help me with my homework.

Answer 1

Step-by-step explanation:

is the same as

$x^5 + 3^5\\x^5 + 243$

Does that make sense

please mark brainest

Answer 2

Given expression :

${\qquad \sf \dashrightarrow{ (x+3)^{5} } }$

We need to simplify it.

We can write the expression as,

${\qquad \sf \dashrightarrow{ (x+3)^{} }{ (x+3)^{} }{ (x+3)^{} }{ (x+3)^{} }{ (x+3)^{} }}$

${\qquad \sf \dashrightarrow{ (x+3)^{2} }{ (x+3)^{2} }{ (x+3)^{} }}$

We know that,

${\qquad \sf \dashrightarrow{ (a+b)^{2} } = {a}^{2} + 2ab + {b}^{2} }$

Now, using the formula in the expression:

${\qquad \sf \dashrightarrow{ (x {}^{2} + 2x.3 +3^{2}) }{ (x {}^{2} + 2x.3 +3^{2}) }{ (x+3)^{} }}$

${\qquad \sf \dashrightarrow{ (x {}^{2} + 6x +9) }{ (x {}^{2} + 6x +9) }{ (x+3)^{} }}$

${\qquad \sf \dashrightarrow{ ( {x}^{4} + 6 {x}^{3} + 9 {x }^{2} + 6x {}^{3} + 36 {x}^{2} + 54x + 9 {x}^{2} + 54x + 81 ) }{ (x+3)^{} }}$

${\qquad \sf \dashrightarrow{ ( {x}^{4} + 12{x}^{3} + 54 {x }^{2} + 108x + 81 ) }{ (x+3)^{} }}$

${\qquad \sf \dashrightarrow{ \: {x}^{5} + 12 {x}^{4} + 54 {x}^{3} + 108 {x}^{2} + 81x + 3 {x}^{4} + 36x {}^{3} + 162 {x}^{2} + 324x + 243 }}$

Adding the like terms we get :

${\qquad \sf \dashrightarrow{ \: {x}^{5} + 15 {x}^{4} + 90 {x}^{3} + 270 {x}^{2} + 405x + 243 }}$