How do you multiply ${(x + 7)}^{4}$ $(x+7)^4$ ?

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Answer 1 · 2015-08-08T13:44:50

$x^{4} + 28 x^{3} + 294 x^{2} + 1372 x + 2401$ $x^4 + 28x^3 + 294x^2 + 1372x + 2401$

Using the first 5 rows of Pascal's Triangle:
${: (0, ":", 1,,,,), (1, ":", 1, 1,,,), (2,":", 1,2, 1,,), (3,":",1,3,3,1,), (4,":",1,4,6,4,1) :}$

$(a+b)^4 = 1a^4b^0+4a^3b^1+6a^2b^2+4a^1b^3+1a^0b^4$

Substituting $x$ for $a$ and $7$ for $b$

$(x+7)^4$
$color(white)("XXXX")$ $= x^4 + 4x^3(7^1)+6x^2(7^2)+4x(7^3) + 1(7^4)$

$color(white)("XXXX")$ $=x^4 + 28x^3 + 294x^2 + 1372x + 2401$

How do you multiply (x+7)^4(x+7)4(x+7)^4?