Write in Standard Form (x+3)(x+4)(x+5)

$(x + 3) (x + 4) (x + 5)$

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 $(x + 3) (x + 4)$ using the FOIL Method.

Apply the distributive property.

$(x (x + 4) + 3 (x + 4)) (x + 5)$

Apply the distributive property.

$(x \cdot x + x \cdot 4 + 3 (x + 4)) (x + 5)$

Apply the distributive property.

$(x \cdot x + x \cdot 4 + 3 x + 3 \cdot 4) (x + 5)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $4$ to the left of $x$ .

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

Multiply $3$ by $4$ .

$(x^{2} + 4 x + 3 x + 12) (x + 5)$

Add $4 x$ and $3 x$ .

$(x^{2} + 7 x + 12) (x + 5)$

Step 4

Expand $(x^{2} + 7 x + 12) (x + 5)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} x + x^{2} \cdot 5 + 7 x \cdot x + 7 x \cdot 5 + 12 x + 12 \cdot 5$

Step 5

Simplify terms.

Simplify each term.

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

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

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

$x^{2} x^{1} + x^{2} \cdot 5 + 7 x \cdot x + 7 x \cdot 5 + 12 x + 12 \cdot 5$

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

$x^{2 + 1} + x^{2} \cdot 5 + 7 x \cdot x + 7 x \cdot 5 + 12 x + 12 \cdot 5$

Add $2$ and $1$ .

$x^{3} + x^{2} \cdot 5 + 7 x \cdot x + 7 x \cdot 5 + 12 x + 12 \cdot 5$

Move $5$ to the left of $x^{2}$ .

$x^{3} + 5 \cdot x^{2} + 7 x \cdot x + 7 x \cdot 5 + 12 x + 12 \cdot 5$

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

Move $x$ .

$x^{3} + 5 x^{2} + 7 (x \cdot x) + 7 x \cdot 5 + 12 x + 12 \cdot 5$

Multiply $x$ by $x$ .

$x^{3} + 5 x^{2} + 7 x^{2} + 7 x \cdot 5 + 12 x + 12 \cdot 5$

Multiply $5$ by $7$ .

$x^{3} + 5 x^{2} + 7 x^{2} + 35 x + 12 x + 12 \cdot 5$

Multiply $12$ by $5$ .

$x^{3} + 5 x^{2} + 7 x^{2} + 35 x + 12 x + 60$

Simplify by adding terms.

Add $5 x^{2}$ and $7 x^{2}$ .

$x^{3} + 12 x^{2} + 35 x + 12 x + 60$

Add $35 x$ and $12 x$ .

$x^{3} + 12 x^{2} + 47 x + 60$

Write in Standard Form (x+3)(x+4)(x+5)

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