Trigonometry Examples

$(0.7 x^{2} + 0.4 x - 0.9) (0.9 x^{2} + 1.7)$

Step 1

Expand $(0.7 x^{2} + 0.4 x - 0.9) (0.9 x^{2} + 1.7)$ by multiplying each term in the first expression by each term in the second expression.

$0.7 x^{2} (0.9 x^{2}) + 0.7 x^{2} \cdot 1.7 + 0.4 x (0.9 x^{2}) + 0.4 x \cdot 1.7 - 0.9 (0.9 x^{2}) - 0.9 \cdot 1.7$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$0.7 \cdot 0.9 x^{2} x^{2} + 0.7 x^{2} \cdot 1.7 + 0.4 x (0.9 x^{2}) + 0.4 x \cdot 1.7 - 0.9 (0.9 x^{2}) - 0.9 \cdot 1.7$

Step 2.1.2

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

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Step 2.1.2.1

Move $x^{2}$ .

$0.7 \cdot 0.9 (x^{2} x^{2}) + 0.7 x^{2} \cdot 1.7 + 0.4 x (0.9 x^{2}) + 0.4 x \cdot 1.7 - 0.9 (0.9 x^{2}) - 0.9 \cdot 1.7$

Step 2.1.2.2

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

$0.7 \cdot 0.9 x^{2 + 2} + 0.7 x^{2} \cdot 1.7 + 0.4 x (0.9 x^{2}) + 0.4 x \cdot 1.7 - 0.9 (0.9 x^{2}) - 0.9 \cdot 1.7$

Step 2.1.2.3

Add $2$ and $2$ .

$0.7 \cdot 0.9 x^{4} + 0.7 x^{2} \cdot 1.7 + 0.4 x (0.9 x^{2}) + 0.4 x \cdot 1.7 - 0.9 (0.9 x^{2}) - 0.9 \cdot 1.7$

Step 2.1.3

Multiply $0.7$ by $0.9$ .

$0.63 x^{4} + 0.7 x^{2} \cdot 1.7 + 0.4 x (0.9 x^{2}) + 0.4 x \cdot 1.7 - 0.9 (0.9 x^{2}) - 0.9 \cdot 1.7$

Step 2.1.4

Multiply $1.7$ by $0.7$ .

$0.63 x^{4} + 1.19 x^{2} + 0.4 x (0.9 x^{2}) + 0.4 x \cdot 1.7 - 0.9 (0.9 x^{2}) - 0.9 \cdot 1.7$

Step 2.1.5

Rewrite using the commutative property of multiplication.

$0.63 x^{4} + 1.19 x^{2} + 0.4 \cdot 0.9 x \cdot x^{2} + 0.4 x \cdot 1.7 - 0.9 (0.9 x^{2}) - 0.9 \cdot 1.7$

Step 2.1.6

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

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Step 2.1.6.1

Move $x^{2}$ .

$0.63 x^{4} + 1.19 x^{2} + 0.4 \cdot 0.9 (x^{2} x) + 0.4 x \cdot 1.7 - 0.9 (0.9 x^{2}) - 0.9 \cdot 1.7$

Step 2.1.6.2

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

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Step 2.1.6.2.1

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

$0.63 x^{4} + 1.19 x^{2} + 0.4 \cdot 0.9 (x^{2} x^{1}) + 0.4 x \cdot 1.7 - 0.9 (0.9 x^{2}) - 0.9 \cdot 1.7$

Step 2.1.6.2.2

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

$0.63 x^{4} + 1.19 x^{2} + 0.4 \cdot 0.9 x^{2 + 1} + 0.4 x \cdot 1.7 - 0.9 (0.9 x^{2}) - 0.9 \cdot 1.7$

Step 2.1.6.3

Add $2$ and $1$ .

$0.63 x^{4} + 1.19 x^{2} + 0.4 \cdot 0.9 x^{3} + 0.4 x \cdot 1.7 - 0.9 (0.9 x^{2}) - 0.9 \cdot 1.7$

Step 2.1.7

Multiply $0.4$ by $0.9$ .

$0.63 x^{4} + 1.19 x^{2} + 0.36 x^{3} + 0.4 x \cdot 1.7 - 0.9 (0.9 x^{2}) - 0.9 \cdot 1.7$

Step 2.1.8

Multiply $1.7$ by $0.4$ .

$0.63 x^{4} + 1.19 x^{2} + 0.36 x^{3} + 0.68 x - 0.9 (0.9 x^{2}) - 0.9 \cdot 1.7$

Step 2.1.9

Multiply $0.9$ by $- 0.9$ .

$0.63 x^{4} + 1.19 x^{2} + 0.36 x^{3} + 0.68 x - 0.81 x^{2} - 0.9 \cdot 1.7$

Step 2.1.10

Multiply $- 0.9$ by $1.7$ .

$0.63 x^{4} + 1.19 x^{2} + 0.36 x^{3} + 0.68 x - 0.81 x^{2} - 1.53$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $0.81 x^{2}$ from $1.19 x^{2}$ .

$0.63 x^{4} + 0.38 x^{2} + 0.36 x^{3} + 0.68 x - 1.53$

Step 2.2.2

Move $0.38 x^{2}$ .

$0.63 x^{4} + 0.36 x^{3} + 0.38 x^{2} + 0.68 x - 1.53$