Simplify (2x+3)(4x^2-6x+9)

$(2 x + 3) (4 x^{2} - 6 x + 9)$

Step 1

Expand $(2 x + 3) (4 x^{2} - 6 x + 9)$ by multiplying each term in the first expression by each term in the second expression.

$2 x (4 x^{2}) + 2 x (- 6 x) + 2 x \cdot 9 + 3 (4 x^{2}) + 3 (- 6 x) + 3 \cdot 9$

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 4 x \cdot x^{2} + 2 x (- 6 x) + 2 x \cdot 9 + 3 (4 x^{2}) + 3 (- 6 x) + 3 \cdot 9$

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

Move $x^{2}$ .

$2 \cdot 4 (x^{2} x) + 2 x (- 6 x) + 2 x \cdot 9 + 3 (4 x^{2}) + 3 (- 6 x) + 3 \cdot 9$

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

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

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

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

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

Add $2$ and $1$ .

$2 \cdot 4 x^{3} + 2 x (- 6 x) + 2 x \cdot 9 + 3 (4 x^{2}) + 3 (- 6 x) + 3 \cdot 9$

Multiply $2$ by $4$ .

$8 x^{3} + 2 x (- 6 x) + 2 x \cdot 9 + 3 (4 x^{2}) + 3 (- 6 x) + 3 \cdot 9$

Rewrite using the commutative property of multiplication.

$8 x^{3} + 2 \cdot - 6 x \cdot x + 2 x \cdot 9 + 3 (4 x^{2}) + 3 (- 6 x) + 3 \cdot 9$

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

Move $x$ .

$8 x^{3} + 2 \cdot - 6 (x \cdot x) + 2 x \cdot 9 + 3 (4 x^{2}) + 3 (- 6 x) + 3 \cdot 9$

Multiply $x$ by $x$ .

$8 x^{3} + 2 \cdot - 6 x^{2} + 2 x \cdot 9 + 3 (4 x^{2}) + 3 (- 6 x) + 3 \cdot 9$

Multiply $2$ by $- 6$ .

$8 x^{3} - 12 x^{2} + 2 x \cdot 9 + 3 (4 x^{2}) + 3 (- 6 x) + 3 \cdot 9$

Multiply $9$ by $2$ .

$8 x^{3} - 12 x^{2} + 18 x + 3 (4 x^{2}) + 3 (- 6 x) + 3 \cdot 9$

Multiply $4$ by $3$ .

$8 x^{3} - 12 x^{2} + 18 x + 12 x^{2} + 3 (- 6 x) + 3 \cdot 9$

Multiply $- 6$ by $3$ .

$8 x^{3} - 12 x^{2} + 18 x + 12 x^{2} - 18 x + 3 \cdot 9$

Multiply $3$ by $9$ .

$8 x^{3} - 12 x^{2} + 18 x + 12 x^{2} - 18 x + 27$

Combine the opposite terms in $8 x^{3} - 12 x^{2} + 18 x + 12 x^{2} - 18 x + 27$ .

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

$8 x^{3} + 18 x + 0 - 18 x + 27$

Add $8 x^{3} + 18 x$ and $0$ .

$8 x^{3} + 18 x - 18 x + 27$

Subtract $18 x$ from $18 x$ .

$8 x^{3} + 0 + 27$

Add $8 x^{3}$ and $0$ .

$8 x^{3} + 27$

Simplify (2x+3)(4x^2-6x+9)

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