Simplify (2x-1)(2x^2+5x+3)+(3x+6)

$(2 x - 1) (2 x^{2} + 5 x + 3) + (3 x + 6)$

Step 1

Remove parentheses.

$(2 x - 1) (2 x^{2} + 5 x + 3) + 3 x + 6$

Step 2

Simplify each term.

Expand $(2 x - 1) (2 x^{2} + 5 x + 3)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $5$ .

$4 x^{3} + 10 x^{2} + 2 x \cdot 3 - 1 (2 x^{2}) - 1 (5 x) - 1 \cdot 3 + 3 x + 6$

Multiply $3$ by $2$ .

$4 x^{3} + 10 x^{2} + 6 x - 1 (2 x^{2}) - 1 (5 x) - 1 \cdot 3 + 3 x + 6$

Multiply $2$ by $- 1$ .

$4 x^{3} + 10 x^{2} + 6 x - 2 x^{2} - 1 (5 x) - 1 \cdot 3 + 3 x + 6$

Multiply $5$ by $- 1$ .

$4 x^{3} + 10 x^{2} + 6 x - 2 x^{2} - 5 x - 1 \cdot 3 + 3 x + 6$

Multiply $- 1$ by $3$ .

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

Subtract $2 x^{2}$ from $10 x^{2}$ .

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

Subtract $5 x$ from $6 x$ .

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

Step 3

Simplify by adding terms.

Add $x$ and $3 x$ .

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

Add $- 3$ and $6$ .

$4 x^{3} + 8 x^{2} + 4 x + 3$

Simplify (2x-1)(2x^2+5x+3)+(3x+6)

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