What is expand (4x^2-4x)*(1+Δx) ?

The solution to expand (4x^2-4x)*(1+Δx) is 4x^2+4Δx^3-4x-4Δx^2

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expand (4x^2-4x)*(1+Δx)

expand

(4 x^{2} - 4 x) \cdot (1 + Δ x)

4 x^{2} + 4Δ x^{3} - 4 x - 4Δ x^{2}

Solution steps

(4 x^{2} - 4 x) (1 + Δ x)

Apply FOIL method:

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

a = 4 x^{2}, b = - 4 x, c = 1, d = Δ x

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

Apply minus-plus rules

+ (- a) = - a

= 4 \cdot 1 \cdot x^{2} + 4Δ x^{2} x - 4 \cdot 1 \cdot x - 4Δ xx

Simplify

4 \cdot 1 \cdot x^{2} + 4Δ x^{2} x - 4 \cdot 1 \cdot x - 4Δ xx : 4 x^{2} + 4Δ x^{3} - 4 x - 4Δ x^{2}

= 4 x^{2} + 4Δ x^{3} - 4 x - 4Δ x^{2}

(- x + 4 \circ - x + 4) (- 1)

(2 x + 5 + 1)^{2}

(cos (x) - 1) (1 - cos (x))

96 a 2 - 48 a 2 m + 144 a 2 n 2

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

What is expand (4x^2-4x)*(1+Δx) ?
The solution to expand (4x^2-4x)*(1+Δx) is 4x^2+4Δx^3-4x-4Δx^2