Simplify (-3s+2t)(4s-t)

$(- 3 s + 2 t) (4 s - t)$

Step 1

Expand $(- 3 s + 2 t) (4 s - t)$ using the FOIL Method.

Apply the distributive property.

$- 3 s (4 s - t) + 2 t (4 s - t)$

Apply the distributive property.

$- 3 s (4 s) - 3 s (- t) + 2 t (4 s - t)$

Apply the distributive property.

$- 3 s (4 s) - 3 s (- t) + 2 t (4 s) + 2 t (- t)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 3 \cdot 4 s \cdot s - 3 s (- t) + 2 t (4 s) + 2 t (- t)$

Multiply $s$ by $s$ by adding the exponents.

Move $s$ .

$- 3 \cdot 4 (s \cdot s) - 3 s (- t) + 2 t (4 s) + 2 t (- t)$

Multiply $s$ by $s$ .

$- 3 \cdot 4 s^{2} - 3 s (- t) + 2 t (4 s) + 2 t (- t)$

Multiply $- 3$ by $4$ .

$- 12 s^{2} - 3 s (- t) + 2 t (4 s) + 2 t (- t)$

Rewrite using the commutative property of multiplication.

$- 12 s^{2} - 3 \cdot - 1 s t + 2 t (4 s) + 2 t (- t)$

Multiply $- 3$ by $- 1$ .

$- 12 s^{2} + 3 s t + 2 t (4 s) + 2 t (- t)$

Rewrite using the commutative property of multiplication.

$- 12 s^{2} + 3 s t + 2 \cdot 4 t s + 2 t (- t)$

Multiply $2$ by $4$ .

$- 12 s^{2} + 3 s t + 8 t s + 2 t (- t)$

Rewrite using the commutative property of multiplication.

$- 12 s^{2} + 3 s t + 8 t s + 2 \cdot - 1 t \cdot t$

Multiply $t$ by $t$ by adding the exponents.

Move $t$ .

$- 12 s^{2} + 3 s t + 8 t s + 2 \cdot - 1 (t \cdot t)$

Multiply $t$ by $t$ .

$- 12 s^{2} + 3 s t + 8 t s + 2 \cdot - 1 t^{2}$

Multiply $2$ by $- 1$ .

$- 12 s^{2} + 3 s t + 8 t s - 2 t^{2}$

Add $3 s t$ and $8 t s$ .

Move $t$ .

$- 12 s^{2} + 3 s t + 8 s t - 2 t^{2}$

Add $3 s t$ and $8 s t$ .

$- 12 s^{2} + 11 s t - 2 t^{2}$