Trigonometry Examples

$(- 3 x^{2} \cdot (7 x^{2}) - 8) - (- 5 x^{3} + 9 x^{2} - 8 - 19)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$- 3 \cdot 7 x^{2} x^{2} - 8 - (- 5 x^{3} + 9 x^{2} - 8 - 19)$

Step 2.2

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

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Step 2.2.1

Move $x^{2}$ .

$- 3 \cdot 7 (x^{2} x^{2}) - 8 - (- 5 x^{3} + 9 x^{2} - 8 - 19)$

Step 2.2.2

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

$- 3 \cdot 7 x^{2 + 2} - 8 - (- 5 x^{3} + 9 x^{2} - 8 - 19)$

Step 2.2.3

Add $2$ and $2$ .

$- 3 \cdot 7 x^{4} - 8 - (- 5 x^{3} + 9 x^{2} - 8 - 19)$

Step 2.3

Multiply $- 3$ by $7$ .

$- 21 x^{4} - 8 - (- 5 x^{3} + 9 x^{2} - 8 - 19)$

Step 2.4

Subtract $19$ from $- 8$ .

$- 21 x^{4} - 8 - (- 5 x^{3} + 9 x^{2} - 27)$

Step 2.5

Apply the distributive property.

$- 21 x^{4} - 8 - (- 5 x^{3}) - (9 x^{2}) - - 27$

Step 2.6

Simplify.

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Step 2.6.1

Multiply $- 5$ by $- 1$ .

$- 21 x^{4} - 8 + 5 x^{3} - (9 x^{2}) - - 27$

Step 2.6.2

Multiply $9$ by $- 1$ .

$- 21 x^{4} - 8 + 5 x^{3} - 9 x^{2} - - 27$

Step 2.6.3

Multiply $- 1$ by $- 27$ .

$- 21 x^{4} - 8 + 5 x^{3} - 9 x^{2} + 27$

Step 3

Add $- 8$ and $27$ .

$- 21 x^{4} + 5 x^{3} - 9 x^{2} + 19$