Write in Standard Form (x+2)(2x+1)(4x-5)

$(x + 2) (2 x + 1) (4 x - 5)$

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

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

Apply the distributive property.

$(x (2 x + 1) + 2 (2 x + 1)) (4 x - 5)$

Apply the distributive property.

$(x (2 x) + x \cdot 1 + 2 (2 x + 1)) (4 x - 5)$

Apply the distributive property.

$(x (2 x) + x \cdot 1 + 2 (2 x) + 2 \cdot 1) (4 x - 5)$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$(2 x \cdot x + x \cdot 1 + 2 (2 x) + 2 \cdot 1) (4 x - 5)$

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

Move $x$ .

$(2 (x \cdot x) + x \cdot 1 + 2 (2 x) + 2 \cdot 1) (4 x - 5)$

Multiply $x$ by $x$ .

$(2 x^{2} + x \cdot 1 + 2 (2 x) + 2 \cdot 1) (4 x - 5)$

Multiply $x$ by $1$ .

$(2 x^{2} + x + 2 (2 x) + 2 \cdot 1) (4 x - 5)$

Multiply $2$ by $2$ .

$(2 x^{2} + x + 4 x + 2 \cdot 1) (4 x - 5)$

Multiply $2$ by $1$ .

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

Add $x$ and $4 x$ .

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

Step 4

Expand $(2 x^{2} + 5 x + 2) (4 x - 5)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 5

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

$2 \cdot 4 (x^{1} x^{2}) + 2 x^{2} \cdot - 5 + 5 x (4 x) + 5 x \cdot - 5 + 2 (4 x) + 2 \cdot - 5$

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

$2 \cdot 4 x^{1 + 2} + 2 x^{2} \cdot - 5 + 5 x (4 x) + 5 x \cdot - 5 + 2 (4 x) + 2 \cdot - 5$

Add $1$ and $2$ .

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

Multiply $2$ by $4$ .

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

Multiply $- 5$ by $2$ .

$8 x^{3} - 10 x^{2} + 5 x (4 x) + 5 x \cdot - 5 + 2 (4 x) + 2 \cdot - 5$

Rewrite using the commutative property of multiplication.

$8 x^{3} - 10 x^{2} + 5 \cdot 4 x \cdot x + 5 x \cdot - 5 + 2 (4 x) + 2 \cdot - 5$

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

Move $x$ .

$8 x^{3} - 10 x^{2} + 5 \cdot 4 (x \cdot x) + 5 x \cdot - 5 + 2 (4 x) + 2 \cdot - 5$

Multiply $x$ by $x$ .

$8 x^{3} - 10 x^{2} + 5 \cdot 4 x^{2} + 5 x \cdot - 5 + 2 (4 x) + 2 \cdot - 5$

Multiply $5$ by $4$ .

$8 x^{3} - 10 x^{2} + 20 x^{2} + 5 x \cdot - 5 + 2 (4 x) + 2 \cdot - 5$

Multiply $- 5$ by $5$ .

$8 x^{3} - 10 x^{2} + 20 x^{2} - 25 x + 2 (4 x) + 2 \cdot - 5$

Multiply $4$ by $2$ .

$8 x^{3} - 10 x^{2} + 20 x^{2} - 25 x + 8 x + 2 \cdot - 5$

Multiply $2$ by $- 5$ .

$8 x^{3} - 10 x^{2} + 20 x^{2} - 25 x + 8 x - 10$

Simplify by adding terms.

Add $- 10 x^{2}$ and $20 x^{2}$ .

$8 x^{3} + 10 x^{2} - 25 x + 8 x - 10$

Add $- 25 x$ and $8 x$ .

$8 x^{3} + 10 x^{2} - 17 x - 10$

Write in Standard Form (x+2)(2x+1)(4x-5)

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