Answer:
[tex]\huge\boxed{ \sf x^4+28x^3+294x^2+1372x+2401}[/tex]
explanation:
[tex]\sf (x+7)^4[/tex]
[tex]\hookrightarrow \sf (x+7) (x+7) (x+7) (x+7)[/tex]
[tex]\hookrightarrow \sf (x^2 +14x+49)(x+7)(x+7)[/tex]
[tex]\hookrightarrow \sf (x^3 +14x^2+49x+7x^2+98x+343)(x+7)[/tex]
[tex]\hookrightarrow \sf (x^3 +21x^2 +147x +343)(x+7)[/tex]
[tex]\hookrightarrow \sf x^4 + 21 x^3 + 147x^2 + 343x + 7x^3 + 147x^2 + 1029x+ 2401[/tex]
[tex]\hookrightarrow \sf x^4+28x^3+294x^2+1372x+2401[/tex]
note: just keep multiplying and simplifying with patience.
[tex](x + 7)^{4} [/tex]
Write 4 as a sum
[tex] {(x + 7)}^{2 + 2} [/tex]
Use [tex] \boxed{ \pmb{ {a}^{m + n} = {a}^{m} \times {a}^{n} }}[/tex] to expand the expression
[tex] {(x + 7)}^{2} \times {(x + 7)}^{2} [/tex]
Use [tex] \boxed{ \pmb{(a + b)^{2} = {a}^{2} + 2ab + {b}^{2} }}[/tex] to expand the expression
[tex] ( {x}^{2} + 14x + 49) \times ( {x}^{2} + 14x + 49)[/tex]
Multiply the parentheses
[tex] {x}^{4} + 14 {x}^{3} + {49x}^{2} + 14 {x}^{3} + {196x}^{2} + 686x + {49x}^{2} + 686x + 2401[/tex]
Collect like terms
[tex] {x}^{4} + {28x}^{3} + {294x}^{2} + 1372x + 2401[/tex]
