What is expand (x^2-5ex+3)(x^3+2x+1) ?

The solution to expand (x^2-5ex+3)(x^3+2x+1) is x^5-5ex^4+5x^3-10ex^2+x^2-5ex+6x+3

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expand (x^2-5ex+3)(x^3+2x+1)

expand

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

x^{5} - 5 e x^{4} + 5 x^{3} - 10 e x^{2} + x^{2} - 5 e x + 6 x + 3

Solution steps

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

Distribute parentheses

= x^{2} x^{3} + x^{2} \cdot 2 x + x^{2} \cdot 1 + (- 5 e x) x^{3} + (- 5 e x) \cdot 2 x + (- 5 e x) \cdot 1 + 3 x^{3} + 3 \cdot 2 x + 3 \cdot 1

Apply minus-plus rules

+ (- a) = - a

= x^{3} x^{2} + 2 x^{2} x + 1 \cdot x^{2} - 5 e x^{3} x - 5 \cdot 2 e xx - 5 \cdot 1 e x + 3 x^{3} + 3 \cdot 2 x + 3 \cdot 1

Simplify

x^{3} x^{2} + 2 x^{2} x + 1 \cdot x^{2} - 5 e x^{3} x - 5 \cdot 2 e xx - 5 \cdot 1 e x + 3 x^{3} + 3 \cdot 2 x + 3 \cdot 1 : x^{5} - 5 e x^{4} + 5 x^{3} - 10 e x^{2} + x^{2} - 5 e x + 6 x + 3

= x^{5} - 5 e x^{4} + 5 x^{3} - 10 e x^{2} + x^{2} - 5 e x + 6 x + 3

1 + (\frac{( x ^{4} + 9 )}{( 18 x )})^{2}

(bi + c j + d k)^{2}

(1 + e^{x}) d x

\frac{- 6 x ^{2} - 43 x + 103}{( x + 5 ) ( x + 2 ) ( x + 13 )}

(x^{2} - 2 x y + y^{2} = 3) (- 1)

What is expand (x^2-5ex+3)(x^3+2x+1) ?
The solution to expand (x^2-5ex+3)(x^3+2x+1) is x^5-5ex^4+5x^3-10ex^2+x^2-5ex+6x+3