Expand the Trigonometric Expression (1-4m)(m^2-3m+8)

$(1 - 4 m) (m^{2} - 3 m + 8)$

Step 1

Expand $(1 - 4 m) (m^{2} - 3 m + 8)$ by multiplying each term in the first expression by each term in the second expression.

$1 m^{2} + 1 (- 3 m) + 1 \cdot 8 - 4 m \cdot m^{2} - 4 m (- 3 m) - 4 m \cdot 8$

Step 2

Simplify terms.

Simplify each term.

Multiply $m^{2}$ by $1$ .

$m^{2} + 1 (- 3 m) + 1 \cdot 8 - 4 m \cdot m^{2} - 4 m (- 3 m) - 4 m \cdot 8$

Multiply $- 3 m$ by $1$ .

$m^{2} - 3 m + 1 \cdot 8 - 4 m \cdot m^{2} - 4 m (- 3 m) - 4 m \cdot 8$

Multiply $8$ by $1$ .

$m^{2} - 3 m + 8 - 4 m \cdot m^{2} - 4 m (- 3 m) - 4 m \cdot 8$

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

Move $m^{2}$ .

$m^{2} - 3 m + 8 - 4 (m^{2} m) - 4 m (- 3 m) - 4 m \cdot 8$

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

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

$m^{2} - 3 m + 8 - 4 (m^{2} m^{1}) - 4 m (- 3 m) - 4 m \cdot 8$

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

$m^{2} - 3 m + 8 - 4 m^{2 + 1} - 4 m (- 3 m) - 4 m \cdot 8$

Add $2$ and $1$ .

$m^{2} - 3 m + 8 - 4 m^{3} - 4 m (- 3 m) - 4 m \cdot 8$

Rewrite using the commutative property of multiplication.

$m^{2} - 3 m + 8 - 4 m^{3} - 4 \cdot - 3 m \cdot m - 4 m \cdot 8$

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$m^{2} - 3 m + 8 - 4 m^{3} - 4 \cdot - 3 (m \cdot m) - 4 m \cdot 8$

Multiply $m$ by $m$ .

$m^{2} - 3 m + 8 - 4 m^{3} - 4 \cdot - 3 m^{2} - 4 m \cdot 8$

Multiply $- 4$ by $- 3$ .

$m^{2} - 3 m + 8 - 4 m^{3} + 12 m^{2} - 4 m \cdot 8$

Multiply $8$ by $- 4$ .

$m^{2} - 3 m + 8 - 4 m^{3} + 12 m^{2} - 32 m$

Simplify by adding terms.

Add $m^{2}$ and $12 m^{2}$ .

$13 m^{2} - 3 m + 8 - 4 m^{3} - 32 m$

Subtract $32 m$ from $- 3 m$ .

$13 m^{2} - 35 m + 8 - 4 m^{3}$