Question

Please help with homework. My question is: le="(x+7)^{4}" alt="(x+7)^{4}" align="absmiddle" class="latex-formula">
Help ASAP! Please! :(

Answer 1

$(x + 7)^{4}$

Write 4 as a sum

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

Use $\boxed{ \pmb{ {a}^{m + n} = {a}^{m} \times {a}^{n} }}$ to expand the expression

${(x + 7)}^{2} \times {(x + 7)}^{2}$

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

$( {x}^{2} + 14x + 49) \times ( {x}^{2} + 14x + 49)$

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

Answer:

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

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.