What is ((2k)!)/(k!)+k!(4k+2) ?

The solution to ((2k)!)/(k!)+k!(4k+2) is (4kk!^2+2k!^2+(2k)!)/(k!)

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simplify ((2k)!)/(k!)+k!(4k+2)

simplify

\frac{( 2 k ) !}{k !} + k! (4 k + 2)

\frac{4 kk ! ^{2} + 2 k ! ^{2} + ( 2 k ) !}{k !}

Solution steps

\frac{( 2 k ) !}{k !} + k! (4 k + 2)

Apply the fraction rule:

a + \frac{b}{c} = \frac{a c + b}{c}

= \frac{k ! ( 4 k + 2 ) k ! + ( 2 k ) !}{k !}

Apply exponent rule:

aa = a^{2}

k! k! = k!^{2}

= \frac{k ! ^{2} ( 4 k + 2 ) + ( 2 k ) !}{k !}

Simplify

k!^{2} (4 k + 2) + (2 k)! : 4 kk!^{2} + 2 k!^{2} + (2 k)!

= \frac{4 kk ! ^{2} + 2 k ! ^{2} + ( 2 k ) !}{k !}

\frac{d}{d t} ((z (t, x, y)) (x^{2} + y^{2} - x y (t)))

(u v^{0}, 3 (x + 5.3)^{3} + 22) \times (10)

(x - 3) x - 3

(5 x^{\frac{1}{3}} + 2) (5 x^{\frac{1}{3}} - 2)

\frac{x ^{2} - 2}{x ( x - 1 ) ^{2}}

What is ((2k)!)/(k!)+k!(4k+2) ?
The solution to ((2k)!)/(k!)+k!(4k+2) is (4kk!^2+2k!^2+(2k)!)/(k!)