Simplify (2x+3)(2x-1)(x+2)(x+2)

$(2 x + 3) (2 x - 1) (x + 2) (x + 2)$

Expand $(2 x + 3) (2 x - 1)$ using the FOIL Method.

Apply the distributive property.

$(2 x (2 x - 1) + 3 (2 x - 1)) (x + 2) (x + 2)$

Apply the distributive property.

$(2 x (2 x) + 2 x \cdot - 1 + 3 (2 x - 1)) (x + 2) (x + 2)$

Apply the distributive property.

$(2 x (2 x) + 2 x \cdot - 1 + 3 (2 x) + 3 \cdot - 1) (x + 2) (x + 2)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$(2 \cdot 2 x \cdot x + 2 x \cdot - 1 + 3 (2 x) + 3 \cdot - 1) (x + 2) (x + 2)$

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

Move $x$ .

$(2 \cdot 2 (x \cdot x) + 2 x \cdot - 1 + 3 (2 x) + 3 \cdot - 1) (x + 2) (x + 2)$

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Multiply $- 1$ by $2$ .

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

Multiply $2$ by $3$ .

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

Multiply $3$ by $- 1$ .

$(4 x^{2} - 2 x + 6 x - 3) (x + 2) (x + 2)$

Add $- 2 x$ and $6 x$ .

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

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

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

Simplify terms.

Simplify each term.

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $2$ by $4$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $4$ .

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

Multiply $- 3$ by $2$ .

$(4 x^{3} + 8 x^{2} + 4 x^{2} + 8 x - 3 x - 6) (x + 2)$

Simplify by adding terms.

Add $8 x^{2}$ and $4 x^{2}$ .

$(4 x^{3} + 12 x^{2} + 8 x - 3 x - 6) (x + 2)$

Subtract $3 x$ from $8 x$ .

$(4 x^{3} + 12 x^{2} + 5 x - 6) (x + 2)$

Expand $(4 x^{3} + 12 x^{2} + 5 x - 6) (x + 2)$ by multiplying each term in the first expression by each term in the second expression.

$4 x^{3} x + 4 x^{3} \cdot 2 + 12 x^{2} x + 12 x^{2} \cdot 2 + 5 x \cdot x + 5 x \cdot 2 - 6 x - 6 \cdot 2$

Simplify terms.

Simplify each term.

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

Move $x$ .

$4 (x \cdot x^{3}) + 4 x^{3} \cdot 2 + 12 x^{2} x + 12 x^{2} \cdot 2 + 5 x \cdot x + 5 x \cdot 2 - 6 x - 6 \cdot 2$

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

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

$4 (x^{1} x^{3}) + 4 x^{3} \cdot 2 + 12 x^{2} x + 12 x^{2} \cdot 2 + 5 x \cdot x + 5 x \cdot 2 - 6 x - 6 \cdot 2$

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

$4 x^{1 + 3} + 4 x^{3} \cdot 2 + 12 x^{2} x + 12 x^{2} \cdot 2 + 5 x \cdot x + 5 x \cdot 2 - 6 x - 6 \cdot 2$

Add $1$ and $3$ .

$4 x^{4} + 4 x^{3} \cdot 2 + 12 x^{2} x + 12 x^{2} \cdot 2 + 5 x \cdot x + 5 x \cdot 2 - 6 x - 6 \cdot 2$

Multiply $2$ by $4$ .

$4 x^{4} + 8 x^{3} + 12 x^{2} x + 12 x^{2} \cdot 2 + 5 x \cdot x + 5 x \cdot 2 - 6 x - 6 \cdot 2$

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

Move $x$ .

$4 x^{4} + 8 x^{3} + 12 (x \cdot x^{2}) + 12 x^{2} \cdot 2 + 5 x \cdot x + 5 x \cdot 2 - 6 x - 6 \cdot 2$

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

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

$4 x^{4} + 8 x^{3} + 12 (x^{1} x^{2}) + 12 x^{2} \cdot 2 + 5 x \cdot x + 5 x \cdot 2 - 6 x - 6 \cdot 2$

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

$4 x^{4} + 8 x^{3} + 12 x^{1 + 2} + 12 x^{2} \cdot 2 + 5 x \cdot x + 5 x \cdot 2 - 6 x - 6 \cdot 2$

Add $1$ and $2$ .

$4 x^{4} + 8 x^{3} + 12 x^{3} + 12 x^{2} \cdot 2 + 5 x \cdot x + 5 x \cdot 2 - 6 x - 6 \cdot 2$

Multiply $2$ by $12$ .

$4 x^{4} + 8 x^{3} + 12 x^{3} + 24 x^{2} + 5 x \cdot x + 5 x \cdot 2 - 6 x - 6 \cdot 2$

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

Move $x$ .

$4 x^{4} + 8 x^{3} + 12 x^{3} + 24 x^{2} + 5 (x \cdot x) + 5 x \cdot 2 - 6 x - 6 \cdot 2$

Multiply $x$ by $x$ .

$4 x^{4} + 8 x^{3} + 12 x^{3} + 24 x^{2} + 5 x^{2} + 5 x \cdot 2 - 6 x - 6 \cdot 2$

Multiply $2$ by $5$ .

$4 x^{4} + 8 x^{3} + 12 x^{3} + 24 x^{2} + 5 x^{2} + 10 x - 6 x - 6 \cdot 2$

Multiply $- 6$ by $2$ .

$4 x^{4} + 8 x^{3} + 12 x^{3} + 24 x^{2} + 5 x^{2} + 10 x - 6 x - 12$

Simplify by adding terms.

Add $8 x^{3}$ and $12 x^{3}$ .

$4 x^{4} + 20 x^{3} + 24 x^{2} + 5 x^{2} + 10 x - 6 x - 12$

Add $24 x^{2}$ and $5 x^{2}$ .

$4 x^{4} + 20 x^{3} + 29 x^{2} + 10 x - 6 x - 12$

Subtract $6 x$ from $10 x$ .

$4 x^{4} + 20 x^{3} + 29 x^{2} + 4 x - 12$

Simplify (2x+3)(2x-1)(x+2)(x+2)

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