Simplify 5x+4x^2(2x+7)-6x^2-9x

$5 x + 4 x^{2} (2 x + 7) - 6 x^{2} - 9 x$

Step 1

Simplify each term.

Apply the distributive property.

$5 x + 4 x^{2} (2 x) + 4 x^{2} \cdot 7 - 6 x^{2} - 9 x$

Rewrite using the commutative property of multiplication.

$5 x + 4 \cdot 2 x^{2} x + 4 x^{2} \cdot 7 - 6 x^{2} - 9 x$

Multiply $7$ by $4$ .

$5 x + 4 \cdot 2 x^{2} x + 28 x^{2} - 6 x^{2} - 9 x$

Simplify each term.

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

Move $x$ .

$5 x + 4 \cdot 2 (x \cdot x^{2}) + 28 x^{2} - 6 x^{2} - 9 x$

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

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

$5 x + 4 \cdot 2 (x^{1} x^{2}) + 28 x^{2} - 6 x^{2} - 9 x$

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

$5 x + 4 \cdot 2 x^{1 + 2} + 28 x^{2} - 6 x^{2} - 9 x$

Add $1$ and $2$ .

$5 x + 4 \cdot 2 x^{3} + 28 x^{2} - 6 x^{2} - 9 x$

Multiply $4$ by $2$ .

$5 x + 8 x^{3} + 28 x^{2} - 6 x^{2} - 9 x$

Step 2

Simplify by adding terms.

Subtract $9 x$ from $5 x$ .

$8 x^{3} + 28 x^{2} - 6 x^{2} - 4 x$

Subtract $6 x^{2}$ from $28 x^{2}$ .

$8 x^{3} + 22 x^{2} - 4 x$