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

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

Step 1

Rewrite ${(3 x - 1)}^{2}$ as $(3 x - 1) (3 x - 1)$ .

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $3$ .

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

Multiply $- 1$ by $3$ .

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

Multiply $3$ by $- 1$ .

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

Multiply $- 1$ by $- 1$ .

$(2 x + 1) (9 x^{2} - 3 x - 3 x + 1)$

Subtract $3 x$ from $- 3 x$ .

$(2 x + 1) (9 x^{2} - 6 x + 1)$

Step 4

Expand $(2 x + 1) (9 x^{2} - 6 x + 1)$ by multiplying each term in the first expression by each term in the second expression.

$2 x (9 x^{2}) + 2 x (- 6 x) + 2 x \cdot 1 + 1 (9 x^{2}) + 1 (- 6 x) + 1 \cdot 1$

Step 5

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 9 x \cdot x^{2} + 2 x (- 6 x) + 2 x \cdot 1 + 1 (9 x^{2}) + 1 (- 6 x) + 1 \cdot 1$

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

Move $x^{2}$ .

$2 \cdot 9 (x^{2} x) + 2 x (- 6 x) + 2 x \cdot 1 + 1 (9 x^{2}) + 1 (- 6 x) + 1 \cdot 1$

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

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

$2 \cdot 9 (x^{2} x^{1}) + 2 x (- 6 x) + 2 x \cdot 1 + 1 (9 x^{2}) + 1 (- 6 x) + 1 \cdot 1$

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

$2 \cdot 9 x^{2 + 1} + 2 x (- 6 x) + 2 x \cdot 1 + 1 (9 x^{2}) + 1 (- 6 x) + 1 \cdot 1$

Add $2$ and $1$ .

$2 \cdot 9 x^{3} + 2 x (- 6 x) + 2 x \cdot 1 + 1 (9 x^{2}) + 1 (- 6 x) + 1 \cdot 1$

Multiply $2$ by $9$ .

$18 x^{3} + 2 x (- 6 x) + 2 x \cdot 1 + 1 (9 x^{2}) + 1 (- 6 x) + 1 \cdot 1$

Rewrite using the commutative property of multiplication.

$18 x^{3} + 2 \cdot - 6 x \cdot x + 2 x \cdot 1 + 1 (9 x^{2}) + 1 (- 6 x) + 1 \cdot 1$

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

Move $x$ .

$18 x^{3} + 2 \cdot - 6 (x \cdot x) + 2 x \cdot 1 + 1 (9 x^{2}) + 1 (- 6 x) + 1 \cdot 1$

Multiply $x$ by $x$ .

$18 x^{3} + 2 \cdot - 6 x^{2} + 2 x \cdot 1 + 1 (9 x^{2}) + 1 (- 6 x) + 1 \cdot 1$

Multiply $2$ by $- 6$ .

$18 x^{3} - 12 x^{2} + 2 x \cdot 1 + 1 (9 x^{2}) + 1 (- 6 x) + 1 \cdot 1$

Multiply $2$ by $1$ .

$18 x^{3} - 12 x^{2} + 2 x + 1 (9 x^{2}) + 1 (- 6 x) + 1 \cdot 1$

Multiply $9 x^{2}$ by $1$ .

$18 x^{3} - 12 x^{2} + 2 x + 9 x^{2} + 1 (- 6 x) + 1 \cdot 1$

Multiply $- 6 x$ by $1$ .

$18 x^{3} - 12 x^{2} + 2 x + 9 x^{2} - 6 x + 1 \cdot 1$

Multiply $1$ by $1$ .

$18 x^{3} - 12 x^{2} + 2 x + 9 x^{2} - 6 x + 1$

Simplify by adding terms.

Add $- 12 x^{2}$ and $9 x^{2}$ .

$18 x^{3} - 3 x^{2} + 2 x - 6 x + 1$

Subtract $6 x$ from $2 x$ .

$18 x^{3} - 3 x^{2} - 4 x + 1$

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

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