Calculus Examples

$(4 x) (10 x - 3) + (5 x^{2} - 3 x) (4)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$4 x (10 x) + 4 x \cdot - 3 + (5 x^{2} - 3 x) (4)$

Step 1.2

Rewrite using the commutative property of multiplication.

$4 \cdot 10 x \cdot x + 4 x \cdot - 3 + (5 x^{2} - 3 x) (4)$

Step 1.3

Multiply $- 3$ by $4$ .

$4 \cdot 10 x \cdot x - 12 x + (5 x^{2} - 3 x) (4)$

Step 1.4

Simplify each term.

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Step 1.4.1

Multiply $x$ by $x$ by adding the exponents.

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Step 1.4.1.1

Move $x$ .

$4 \cdot 10 (x \cdot x) - 12 x + (5 x^{2} - 3 x) (4)$

Step 1.4.1.2

Multiply $x$ by $x$ .

$4 \cdot 10 x^{2} - 12 x + (5 x^{2} - 3 x) (4)$

Step 1.4.2

Multiply $4$ by $10$ .

$40 x^{2} - 12 x + (5 x^{2} - 3 x) (4)$

Step 1.5

Apply the distributive property.

$40 x^{2} - 12 x + 5 x^{2} \cdot 4 - 3 x \cdot 4$

Step 1.6

Multiply $4$ by $5$ .

$40 x^{2} - 12 x + 20 x^{2} - 3 x \cdot 4$

Step 1.7

Multiply $4$ by $- 3$ .

$40 x^{2} - 12 x + 20 x^{2} - 12 x$

Step 2

Simplify by adding terms.

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Step 2.1

Add $40 x^{2}$ and $20 x^{2}$ .

$60 x^{2} - 12 x - 12 x$

Step 2.2

Subtract $12 x$ from $- 12 x$ .

$60 x^{2} - 24 x$