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6 votes
Please help with homework.

My question is:

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

2 Answers

4 votes


(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

User Executeinstaller
by
8.3k points
8 votes

Answer:


\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.

User Cristian Scutaru
by
8.2k points

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