Finite Math Examples

$f (7 x + 5) (5 x + 7) d x$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$(f (7 x) + f \cdot 5) (5 x + 7) d x$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$(7 f x + f \cdot 5) (5 x + 7) d x$

Step 1.2.2

Move $5$ to the left of $f$ .

$(7 f x + 5 \cdot f) (5 x + 7) d x$

Step 2

Expand $(7 f x + 5 f) (5 x + 7)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$(7 f x (5 x + 7) + 5 f (5 x + 7)) d x$

Step 2.2

Apply the distributive property.

$(7 f x (5 x) + 7 f x \cdot 7 + 5 f (5 x + 7)) d x$

Step 2.3

Apply the distributive property.

$(7 f x (5 x) + 7 f x \cdot 7 + 5 f (5 x) + 5 f \cdot 7) d x$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

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Step 3.1.1.1

Move $x$ .

$(7 f (x \cdot x) \cdot 5 + 7 f x \cdot 7 + 5 f (5 x) + 5 f \cdot 7) d x$

Step 3.1.1.2

Multiply $x$ by $x$ .

$(7 f x^{2} \cdot 5 + 7 f x \cdot 7 + 5 f (5 x) + 5 f \cdot 7) d x$

Step 3.1.2

Multiply $5$ by $7$ .

$(35 f x^{2} + 7 f x \cdot 7 + 5 f (5 x) + 5 f \cdot 7) d x$

Step 3.1.3

Multiply $7$ by $7$ .

$(35 f x^{2} + 49 f x + 5 f (5 x) + 5 f \cdot 7) d x$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$(35 f x^{2} + 49 f x + 5 \cdot 5 f x + 5 f \cdot 7) d x$

Step 3.1.5

Multiply $5$ by $5$ .

$(35 f x^{2} + 49 f x + 25 f x + 5 f \cdot 7) d x$

Step 3.1.6

Multiply $7$ by $5$ .

$(35 f x^{2} + 49 f x + 25 f x + 35 f) d x$

Step 3.2

Add $49 f x$ and $25 f x$ .

$(35 f x^{2} + 74 f x + 35 f) d x$

Step 4

Apply the distributive property.

$(35 f x^{2} d + 74 f x d + 35 f d) x$

Step 5

Apply the distributive property.

$35 f x^{2} d x + 74 f x d x + 35 f d x$

Step 6

Simplify.

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Step 6.1

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 6.1.1

Move $x$ .

$35 f (x \cdot x^{2}) d + 74 f x d x + 35 f d x$

Step 6.1.2

Multiply $x$ by $x^{2}$ .

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Step 6.1.2.1

Raise $x$ to the power of $1$ .

$35 f (x^{1} x^{2}) d + 74 f x d x + 35 f d x$

Step 6.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$35 f x^{1 + 2} d + 74 f x d x + 35 f d x$

Step 6.1.3

Add $1$ and $2$ .

$35 f x^{3} d + 74 f x d x + 35 f d x$

Step 6.2

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

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Step 6.2.1

Move $x$ .

$35 f x^{3} d + 74 f (x \cdot x) d + 35 f d x$

Step 6.2.2

Multiply $x$ by $x$ .

$35 f x^{3} d + 74 f x^{2} d + 35 f d x$