What is expand (4xe^x)(D-1)^2 ?

The solution to expand (4xe^x)(D-1)^2 is 4D^2e^xx-8De^xx+4e^xx

Popular >

expand (4xe^x)(D-1)^2

expand

(4 x e^{x}) (D - 1)^{2}

4 D^{2} e^{x} x - 8 D e^{x} x + 4 e^{x} x

Solution steps

(4 x e^{x}) (D - 1)^{2}

Remove parentheses:

(a) = a

= 4 x e^{x} (D - 1)^{2}

(D - 1)^{2} = D^{2} - 2 D + 1

= 4 e^{x} x (D^{2} - 2 D + 1)

= 4 e^{x} x (D^{2} - 2 D + 1)

Distribute parentheses

= 4 x e^{x} D^{2} + 4 x e^{x} (- 2 D) + 4 x e^{x} \cdot 1

Apply minus-plus rules

+ (- a) = - a

= 4 D^{2} e^{x} x - 4 \cdot 2 D e^{x} x + 4 \cdot 1 \cdot e^{x} x

Simplify

4 D^{2} e^{x} x - 4 \cdot 2 D e^{x} x + 4 \cdot 1 \cdot e^{x} x : 4 D^{2} e^{x} x - 8 D e^{x} x + 4 e^{x} x

= 4 D^{2} e^{x} x - 8 D e^{x} x + 4 e^{x} x

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

\frac{x m + y n}{x ( m + n )}

4 (2 x - 3 = 8 (2 x + 5))

\frac{( 6 x - 1 ) ^{3}}{18}

(- 3, - 1) P (- 6 - 3)

What is expand (4xe^x)(D-1)^2 ?
The solution to expand (4xe^x)(D-1)^2 is 4D^2e^xx-8De^xx+4e^xx