Question

Please help with homework.

My question is:

`(x+7)^(4)`
Help ASAP! Please! :(

Answer 1

`(x + 7)^(4)`

Write 4 as a sum

`{(x + 7)}^(2 + 2)`

Use
`\boxed{ \pmb{ {a}^(m + n) = {a}^(m) * {a}^(n) }}` to expand the expression

`{(x + 7)}^(2) * {(x + 7)}^(2)`

Use
`\boxed{ \pmb{(a + b)^(2) = {a}^(2) + 2ab + {b}^(2) }}` to expand the expression

`( {x}^(2) + 14x + 49) * ( {x}^(2) + 14x + 49)`

Multiply the parentheses

`{x}^(4) + 14 {x}^(3) + {49x}^(2) + 14 {x}^(3) + {196x}^(2) + 686x + {49x}^(2) + 686x + 2401`

Collect like terms

`{x}^(4) + {28x}^(3) + {294x}^(2) + 1372x + 2401`

Answer 2

`\huge\boxed{ \sf x^4+28x^3+294x^2+1372x+2401}`

Step-by-step explanation:

`\sf (x+7)^4`

`\hookrightarrow \sf (x+7) (x+7) (x+7) (x+7)`

`\hookrightarrow \sf (x^2 +14x+49)(x+7)(x+7)`

`\hookrightarrow \sf (x^3 +14x^2+49x+7x^2+98x+343)(x+7)`

`\hookrightarrow \sf (x^3 +21x^2 +147x +343)(x+7)`

`\hookrightarrow \sf x^4 + 21 x^3 + 147x^2 + 343x + 7x^3 + 147x^2 + 1029x+ 2401`

`\hookrightarrow \sf x^4+28x^3+294x^2+1372x+2401`

note: just keep multiplying and simplifying with patience.