Simplify square root of (x+1)(x+2)(x+3)(x+4)+1

$\sqrt{(x + 1) (x + 2) (x + 3) (x + 4) + 1}$

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

Apply the distributive property.

$\sqrt{(x (x + 2) + 1 (x + 2)) (x + 3) (x + 4) + 1}$

Apply the distributive property.

$\sqrt{(x \cdot x + x \cdot 2 + 1 (x + 2)) (x + 3) (x + 4) + 1}$

Apply the distributive property.

$\sqrt{(x \cdot x + x \cdot 2 + 1 x + 1 \cdot 2) (x + 3) (x + 4) + 1}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$\sqrt{(x^{2} + x \cdot 2 + 1 x + 1 \cdot 2) (x + 3) (x + 4) + 1}$

Move $2$ to the left of $x$ .

$\sqrt{(x^{2} + 2 \cdot x + 1 x + 1 \cdot 2) (x + 3) (x + 4) + 1}$

Multiply $x$ by $1$ .

$\sqrt{(x^{2} + 2 x + x + 1 \cdot 2) (x + 3) (x + 4) + 1}$

Multiply $2$ by $1$ .

$\sqrt{(x^{2} + 2 x + x + 2) (x + 3) (x + 4) + 1}$

Add $2 x$ and $x$ .

$\sqrt{(x^{2} + 3 x + 2) (x + 3) (x + 4) + 1}$

Expand $(x^{2} + 3 x + 2) (x + 3)$ by multiplying each term in the first expression by each term in the second expression.

$\sqrt{(x^{2} x + x^{2} \cdot 3 + 3 x \cdot x + 3 x \cdot 3 + 2 x + 2 \cdot 3) (x + 4) + 1}$

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 $1$ .

$\sqrt{(x^{2} x^{1} + x^{2} \cdot 3 + 3 x \cdot x + 3 x \cdot 3 + 2 x + 2 \cdot 3) (x + 4) + 1}$

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

$\sqrt{(x^{2 + 1} + x^{2} \cdot 3 + 3 x \cdot x + 3 x \cdot 3 + 2 x + 2 \cdot 3) (x + 4) + 1}$

Add $2$ and $1$ .

$\sqrt{(x^{3} + x^{2} \cdot 3 + 3 x \cdot x + 3 x \cdot 3 + 2 x + 2 \cdot 3) (x + 4) + 1}$

Move $3$ to the left of $x^{2}$ .

$\sqrt{(x^{3} + 3 \cdot x^{2} + 3 x \cdot x + 3 x \cdot 3 + 2 x + 2 \cdot 3) (x + 4) + 1}$

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

Move $x$ .

$\sqrt{(x^{3} + 3 x^{2} + 3 (x \cdot x) + 3 x \cdot 3 + 2 x + 2 \cdot 3) (x + 4) + 1}$

Multiply $x$ by $x$ .

$\sqrt{(x^{3} + 3 x^{2} + 3 x^{2} + 3 x \cdot 3 + 2 x + 2 \cdot 3) (x + 4) + 1}$

Multiply $3$ by $3$ .

$\sqrt{(x^{3} + 3 x^{2} + 3 x^{2} + 9 x + 2 x + 2 \cdot 3) (x + 4) + 1}$

Multiply $2$ by $3$ .

$\sqrt{(x^{3} + 3 x^{2} + 3 x^{2} + 9 x + 2 x + 6) (x + 4) + 1}$

Simplify by adding terms.

Add $3 x^{2}$ and $3 x^{2}$ .

$\sqrt{(x^{3} + 6 x^{2} + 9 x + 2 x + 6) (x + 4) + 1}$

Add $9 x$ and $2 x$ .

$\sqrt{(x^{3} + 6 x^{2} + 11 x + 6) (x + 4) + 1}$

Expand $(x^{3} + 6 x^{2} + 11 x + 6) (x + 4)$ by multiplying each term in the first expression by each term in the second expression.

$\sqrt{x^{3} x + x^{3} \cdot 4 + 6 x^{2} x + 6 x^{2} \cdot 4 + 11 x \cdot x + 11 x \cdot 4 + 6 x + 6 \cdot 4 + 1}$

Simplify terms.

Simplify each term.

Multiply $x^{3}$ by $x$ by adding the exponents.

Multiply $x^{3}$ by $x$ .

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

$\sqrt{x^{3} x^{1} + x^{3} \cdot 4 + 6 x^{2} x + 6 x^{2} \cdot 4 + 11 x \cdot x + 11 x \cdot 4 + 6 x + 6 \cdot 4 + 1}$

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

$\sqrt{x^{3 + 1} + x^{3} \cdot 4 + 6 x^{2} x + 6 x^{2} \cdot 4 + 11 x \cdot x + 11 x \cdot 4 + 6 x + 6 \cdot 4 + 1}$

Add $3$ and $1$ .

$\sqrt{x^{4} + x^{3} \cdot 4 + 6 x^{2} x + 6 x^{2} \cdot 4 + 11 x \cdot x + 11 x \cdot 4 + 6 x + 6 \cdot 4 + 1}$

Move $4$ to the left of $x^{3}$ .

$\sqrt{x^{4} + 4 \cdot x^{3} + 6 x^{2} x + 6 x^{2} \cdot 4 + 11 x \cdot x + 11 x \cdot 4 + 6 x + 6 \cdot 4 + 1}$

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

Move $x$ .

$\sqrt{x^{4} + 4 x^{3} + 6 (x \cdot x^{2}) + 6 x^{2} \cdot 4 + 11 x \cdot x + 11 x \cdot 4 + 6 x + 6 \cdot 4 + 1}$

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

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

$\sqrt{x^{4} + 4 x^{3} + 6 (x^{1} x^{2}) + 6 x^{2} \cdot 4 + 11 x \cdot x + 11 x \cdot 4 + 6 x + 6 \cdot 4 + 1}$

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

$\sqrt{x^{4} + 4 x^{3} + 6 x^{1 + 2} + 6 x^{2} \cdot 4 + 11 x \cdot x + 11 x \cdot 4 + 6 x + 6 \cdot 4 + 1}$

Add $1$ and $2$ .

$\sqrt{x^{4} + 4 x^{3} + 6 x^{3} + 6 x^{2} \cdot 4 + 11 x \cdot x + 11 x \cdot 4 + 6 x + 6 \cdot 4 + 1}$

Multiply $4$ by $6$ .

$\sqrt{x^{4} + 4 x^{3} + 6 x^{3} + 24 x^{2} + 11 x \cdot x + 11 x \cdot 4 + 6 x + 6 \cdot 4 + 1}$

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

Move $x$ .

$\sqrt{x^{4} + 4 x^{3} + 6 x^{3} + 24 x^{2} + 11 (x \cdot x) + 11 x \cdot 4 + 6 x + 6 \cdot 4 + 1}$

Multiply $x$ by $x$ .

$\sqrt{x^{4} + 4 x^{3} + 6 x^{3} + 24 x^{2} + 11 x^{2} + 11 x \cdot 4 + 6 x + 6 \cdot 4 + 1}$

Multiply $4$ by $11$ .

$\sqrt{x^{4} + 4 x^{3} + 6 x^{3} + 24 x^{2} + 11 x^{2} + 44 x + 6 x + 6 \cdot 4 + 1}$

Multiply $6$ by $4$ .

$\sqrt{x^{4} + 4 x^{3} + 6 x^{3} + 24 x^{2} + 11 x^{2} + 44 x + 6 x + 24 + 1}$

Simplify by adding terms.

Add $4 x^{3}$ and $6 x^{3}$ .

$\sqrt{x^{4} + 10 x^{3} + 24 x^{2} + 11 x^{2} + 44 x + 6 x + 24 + 1}$

Add $24 x^{2}$ and $11 x^{2}$ .

$\sqrt{x^{4} + 10 x^{3} + 35 x^{2} + 44 x + 6 x + 24 + 1}$

Add $44 x$ and $6 x$ .

$\sqrt{x^{4} + 10 x^{3} + 35 x^{2} + 50 x + 24 + 1}$

Add $24$ and $1$ .

$\sqrt{x^{4} + 10 x^{3} + 35 x^{2} + 50 x + 25}$

Simplify square root of (x+1)(x+2)(x+3)(x+4)+1

Related Questions

Support LCMGCF.com by disabling your adblocker.