Evaluate (h^2+9h-1)(-4h+3)

$(h^{2} + 9 h - 1) (- 4 h + 3)$

Step 1

Expand $(h^{2} + 9 h - 1) (- 4 h + 3)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $h$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Move $3$ to the left of $h^{2}$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $h$ by $h$ by adding the exponents.

Move $h$ .

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

Multiply $h$ by $h$ .

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

Multiply $9$ by $- 4$ .

$- 4 h^{3} + 3 h^{2} - 36 h^{2} + 9 h \cdot 3 - 1 (- 4 h) - 1 \cdot 3$

Multiply $3$ by $9$ .

$- 4 h^{3} + 3 h^{2} - 36 h^{2} + 27 h - 1 (- 4 h) - 1 \cdot 3$

Multiply $- 4$ by $- 1$ .

$- 4 h^{3} + 3 h^{2} - 36 h^{2} + 27 h + 4 h - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$- 4 h^{3} + 3 h^{2} - 36 h^{2} + 27 h + 4 h - 3$

Simplify by adding terms.

Subtract $36 h^{2}$ from $3 h^{2}$ .

$- 4 h^{3} - 33 h^{2} + 27 h + 4 h - 3$

Add $27 h$ and $4 h$ .

$- 4 h^{3} - 33 h^{2} + 31 h - 3$