What is expand (4x+4δx)*(x^2-4) ?

The solution to expand (4x+4δx)*(x^2-4) is 4x^3-16x+4δx^3-16δx

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expand (4x+4δx)*(x^2-4)

expand

(4 x + 4 δ x) \cdot (x^{2} - 4)

4 x^{3} - 16 x + 4 δ x^{3} - 16 δ x

Solution steps

(4 x + 4 δ x) (x^{2} - 4)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = 4 x, b = 4 δ x, c = x^{2}, d = - 4

= 4 x x^{2} + 4 x (- 4) + 4 δ x x^{2} + 4 δ x (- 4)

Apply minus-plus rules

+ (- a) = - a

= 4 x^{2} x - 4 \cdot 4 x + 4 δ x^{2} x - 4 \cdot 4 δ x

Simplify

4 x^{2} x - 4 \cdot 4 x + 4 δ x^{2} x - 4 \cdot 4 δ x : 4 x^{3} - 16 x + 4 δ x^{3} - 16 δ x

= 4 x^{3} - 16 x + 4 δ x^{3} - 16 δ x

\frac{24}{( s - 2 ) ^{4}}

2 (- 3 x^{2})

\frac{4 x ^{2} - 8 x + 4}{( x + 1 ) ^{2}}

\frac{( - 2 y + 2 ) ^{3}}{3}

e^{x} (- 2 (- e^{- x} x - e^{- x}))

What is expand (4x+4δx)*(x^2-4) ?
The solution to expand (4x+4δx)*(x^2-4) is 4x^3-16x+4δx^3-16δx