Simplify x(4x+5)+3(2x^2-4x+1)

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

Step 1

Simplify each term.

Apply the distributive property.

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

Rewrite using the commutative property of multiplication.

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

Move $5$ to the left of $x$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

Apply the distributive property.

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

Simplify.

Multiply $2$ by $3$ .

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

Multiply $- 4$ by $3$ .

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

Multiply $3$ by $1$ .

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

Step 2

Simplify by adding terms.

Add $4 x^{2}$ and $6 x^{2}$ .

$10 x^{2} + 5 x - 12 x + 3$

Subtract $12 x$ from $5 x$ .

$10 x^{2} - 7 x + 3$