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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Multiply $- 1$ by $2$ .

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

Multiply $2$ by $- 3$ .

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

Multiply $- 3$ by $- 1$ .

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

Subtract $6 x$ from $- 2 x$ .

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

Step 3

Expand $(4 x^{2} - 8 x + 3) (x - 1)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 4

Simplify terms.

Simplify each term.

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $- 1$ by $4$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 1$ by $- 8$ .

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

Multiply $3$ by $- 1$ .

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

Simplify by adding terms.

Subtract $8 x^{2}$ from $- 4 x^{2}$ .

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

Add $8 x$ and $3 x$ .

$(4 x^{3} - 12 x^{2} + 11 x - 3) (2 x + 3)$

Step 5

Expand $(4 x^{3} - 12 x^{2} + 11 x - 3) (2 x + 3)$ by multiplying each term in the first expression by each term in the second expression.

$4 x^{3} (2 x) + 4 x^{3} \cdot 3 - 12 x^{2} (2 x) - 12 x^{2} \cdot 3 + 11 x (2 x) + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

Step 6

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 2 x^{3} x + 4 x^{3} \cdot 3 - 12 x^{2} (2 x) - 12 x^{2} \cdot 3 + 11 x (2 x) + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

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

Move $x$ .

$4 \cdot 2 (x \cdot x^{3}) + 4 x^{3} \cdot 3 - 12 x^{2} (2 x) - 12 x^{2} \cdot 3 + 11 x (2 x) + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

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

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

$4 \cdot 2 (x^{1} x^{3}) + 4 x^{3} \cdot 3 - 12 x^{2} (2 x) - 12 x^{2} \cdot 3 + 11 x (2 x) + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

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

$4 \cdot 2 x^{1 + 3} + 4 x^{3} \cdot 3 - 12 x^{2} (2 x) - 12 x^{2} \cdot 3 + 11 x (2 x) + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

Add $1$ and $3$ .

$4 \cdot 2 x^{4} + 4 x^{3} \cdot 3 - 12 x^{2} (2 x) - 12 x^{2} \cdot 3 + 11 x (2 x) + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

Multiply $4$ by $2$ .

$8 x^{4} + 4 x^{3} \cdot 3 - 12 x^{2} (2 x) - 12 x^{2} \cdot 3 + 11 x (2 x) + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

Multiply $3$ by $4$ .

$8 x^{4} + 12 x^{3} - 12 x^{2} (2 x) - 12 x^{2} \cdot 3 + 11 x (2 x) + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

Rewrite using the commutative property of multiplication.

$8 x^{4} + 12 x^{3} - 12 \cdot 2 x^{2} x - 12 x^{2} \cdot 3 + 11 x (2 x) + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

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

Move $x$ .

$8 x^{4} + 12 x^{3} - 12 \cdot 2 (x \cdot x^{2}) - 12 x^{2} \cdot 3 + 11 x (2 x) + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

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

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

$8 x^{4} + 12 x^{3} - 12 \cdot 2 (x^{1} x^{2}) - 12 x^{2} \cdot 3 + 11 x (2 x) + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

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

$8 x^{4} + 12 x^{3} - 12 \cdot 2 x^{1 + 2} - 12 x^{2} \cdot 3 + 11 x (2 x) + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

Add $1$ and $2$ .

$8 x^{4} + 12 x^{3} - 12 \cdot 2 x^{3} - 12 x^{2} \cdot 3 + 11 x (2 x) + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

Multiply $- 12$ by $2$ .

$8 x^{4} + 12 x^{3} - 24 x^{3} - 12 x^{2} \cdot 3 + 11 x (2 x) + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

Multiply $3$ by $- 12$ .

$8 x^{4} + 12 x^{3} - 24 x^{3} - 36 x^{2} + 11 x (2 x) + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

Rewrite using the commutative property of multiplication.

$8 x^{4} + 12 x^{3} - 24 x^{3} - 36 x^{2} + 11 \cdot 2 x \cdot x + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

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

Move $x$ .

$8 x^{4} + 12 x^{3} - 24 x^{3} - 36 x^{2} + 11 \cdot 2 (x \cdot x) + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

Multiply $x$ by $x$ .

$8 x^{4} + 12 x^{3} - 24 x^{3} - 36 x^{2} + 11 \cdot 2 x^{2} + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

Multiply $11$ by $2$ .

$8 x^{4} + 12 x^{3} - 24 x^{3} - 36 x^{2} + 22 x^{2} + 11 x \cdot 3 - 3 (2 x) - 3 \cdot 3$

Multiply $3$ by $11$ .

$8 x^{4} + 12 x^{3} - 24 x^{3} - 36 x^{2} + 22 x^{2} + 33 x - 3 (2 x) - 3 \cdot 3$

Multiply $2$ by $- 3$ .

$8 x^{4} + 12 x^{3} - 24 x^{3} - 36 x^{2} + 22 x^{2} + 33 x - 6 x - 3 \cdot 3$

Multiply $- 3$ by $3$ .

$8 x^{4} + 12 x^{3} - 24 x^{3} - 36 x^{2} + 22 x^{2} + 33 x - 6 x - 9$

Simplify by adding terms.

Subtract $24 x^{3}$ from $12 x^{3}$ .

$8 x^{4} - 12 x^{3} - 36 x^{2} + 22 x^{2} + 33 x - 6 x - 9$

Add $- 36 x^{2}$ and $22 x^{2}$ .

$8 x^{4} - 12 x^{3} - 14 x^{2} + 33 x - 6 x - 9$

Subtract $6 x$ from $33 x$ .

$8 x^{4} - 12 x^{3} - 14 x^{2} + 27 x - 9$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.