Algebra Examples

$(2 x + 1) (4 - 9 x) - 2 x (3 x + 11)$

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

Expand $(2 x + 1) (4 - 9 x)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

$2 x (4 - 9 x) + 1 (4 - 9 x) - 2 x (3 x + 11)$

Step 2.1.2

Apply the distributive property.

$2 x \cdot 4 + 2 x (- 9 x) + 1 (4 - 9 x) - 2 x (3 x + 11)$

Step 2.1.3

Apply the distributive property.

$2 x \cdot 4 + 2 x (- 9 x) + 1 \cdot 4 + 1 (- 9 x) - 2 x (3 x + 11)$

Step 2.2

Simplify and combine like terms.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Multiply $4$ by $2$ .

$8 x + 2 x (- 9 x) + 1 \cdot 4 + 1 (- 9 x) - 2 x (3 x + 11)$

Step 2.2.1.2

Rewrite using the commutative property of multiplication.

$8 x + 2 \cdot - 9 x \cdot x + 1 \cdot 4 + 1 (- 9 x) - 2 x (3 x + 11)$

Step 2.2.1.3

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

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Step 2.2.1.3.1

Move $x$ .

$8 x + 2 \cdot - 9 (x \cdot x) + 1 \cdot 4 + 1 (- 9 x) - 2 x (3 x + 11)$

Step 2.2.1.3.2

Multiply $x$ by $x$ .

$8 x + 2 \cdot - 9 x^{2} + 1 \cdot 4 + 1 (- 9 x) - 2 x (3 x + 11)$

Step 2.2.1.4

Multiply $2$ by $- 9$ .

$8 x - 18 x^{2} + 1 \cdot 4 + 1 (- 9 x) - 2 x (3 x + 11)$

Step 2.2.1.5

Multiply $4$ by $1$ .

$8 x - 18 x^{2} + 4 + 1 (- 9 x) - 2 x (3 x + 11)$

Step 2.2.1.6

Multiply $- 9 x$ by $1$ .

$8 x - 18 x^{2} + 4 - 9 x - 2 x (3 x + 11)$

Step 2.2.2

Subtract $9 x$ from $8 x$ .

$- x - 18 x^{2} + 4 - 2 x (3 x + 11)$

Step 2.3

Apply the distributive property.

$- x - 18 x^{2} + 4 - 2 x (3 x) - 2 x \cdot 11$

Step 2.4

Rewrite using the commutative property of multiplication.

$- x - 18 x^{2} + 4 - 2 \cdot 3 x \cdot x - 2 x \cdot 11$

Step 2.5

Multiply $11$ by $- 2$ .

$- x - 18 x^{2} + 4 - 2 \cdot 3 x \cdot x - 22 x$

Step 2.6

Simplify each term.

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Step 2.6.1

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

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Step 2.6.1.1

Move $x$ .

$- x - 18 x^{2} + 4 - 2 \cdot 3 (x \cdot x) - 22 x$

Step 2.6.1.2

Multiply $x$ by $x$ .

$- x - 18 x^{2} + 4 - 2 \cdot 3 x^{2} - 22 x$

Step 2.6.2

Multiply $- 2$ by $3$ .

$- x - 18 x^{2} + 4 - 6 x^{2} - 22 x$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $22 x$ from $- x$ .

$- 18 x^{2} + 4 - 6 x^{2} - 23 x$

Step 3.2

Subtract $6 x^{2}$ from $- 18 x^{2}$ .

$- 24 x^{2} + 4 - 23 x$

Step 3.3

Move $4$ .

$- 24 x^{2} - 23 x + 4$