expandir (x-Δx)^4

Solução

expandir

(x - Δ x)^{4}

x^{4} - 4Δ x^{4} + 6 Δ^{2} x^{4} - 4 Δ^{3} x^{4} + Δ^{4} x^{4}

Passos da solução

(x - Δ x)^{4}

Aplicar o teorema do binômio:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = x, b = - Δ x

= i = 0 \sum 4 (i 4) x^{(4 - i)} (- Δ x)^{i}

Expandir a soma

= \frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} (- Δ x)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (- Δ x)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (- Δ x)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (- Δ x)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (- Δ x)^{4}

Simplificar

\frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} (- Δ x)^{0} : x^{4}

Simplificar

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (- Δ x)^{1} : - 4Δ x^{4}

Simplificar

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (- Δ x)^{2} : 6 Δ^{2} x^{4}

Simplificar

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (- Δ x)^{3} : - 4 Δ^{3} x^{4}

Simplificar

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (- Δ x)^{4} : Δ^{4} x^{4}

= x^{4} - 4Δ x^{4} + 6 Δ^{2} x^{4} - 4 Δ^{3} x^{4} + Δ^{4} x^{4}

e x p an d (t + 2) 2^{e t}

e x p an d \frac{1}{( 1 - X ) ( B - X ) ( D - X )}

e x p an d \frac{1}{( x + 1 ) x ^{2}}

e x p an d 4 c - 3

e x p an d 2 e^{2} \cdot (e^{x} + 2 x)