Simplify (r+2t)(8r+t-w)

$(r + 2 t) (8 r + t - w)$

Step 1

Expand $(r + 2 t) (8 r + t - w)$ by multiplying each term in the first expression by each term in the second expression.

$r (8 r) + r t + r (- w) + 2 t (8 r) + 2 t \cdot t + 2 t (- w)$

Step 2

Simplify each term.

Rewrite using the commutative property of multiplication.

$8 r \cdot r + r t + r (- w) + 2 t (8 r) + 2 t \cdot t + 2 t (- w)$

Multiply $r$ by $r$ by adding the exponents.

Move $r$ .

$8 (r \cdot r) + r t + r (- w) + 2 t (8 r) + 2 t \cdot t + 2 t (- w)$

Multiply $r$ by $r$ .

$8 r^{2} + r t + r (- w) + 2 t (8 r) + 2 t \cdot t + 2 t (- w)$

Rewrite using the commutative property of multiplication.

$8 r^{2} + r t - r w + 2 t (8 r) + 2 t \cdot t + 2 t (- w)$

Rewrite using the commutative property of multiplication.

$8 r^{2} + r t - r w + 2 \cdot 8 t r + 2 t \cdot t + 2 t (- w)$

Multiply $2$ by $8$ .

$8 r^{2} + r t - r w + 16 t r + 2 t \cdot t + 2 t (- w)$

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

Move $t$ .

$8 r^{2} + r t - r w + 16 t r + 2 (t \cdot t) + 2 t (- w)$

Multiply $t$ by $t$ .

$8 r^{2} + r t - r w + 16 t r + 2 t^{2} + 2 t (- w)$

Rewrite using the commutative property of multiplication.

$8 r^{2} + r t - r w + 16 t r + 2 t^{2} + 2 \cdot - 1 t w$

Multiply $2$ by $- 1$ .

$8 r^{2} + r t - r w + 16 t r + 2 t^{2} - 2 t w$

Step 3

Add $r t$ and $16 t r$ .

Move $t$ .

$8 r^{2} + r t + 16 r t - r w + 2 t^{2} - 2 t w$

Add $r t$ and $16 r t$ .

$8 r^{2} + 17 r t - r w + 2 t^{2} - 2 t w$

Step 4

Move $2 t^{2}$ .

$8 r^{2} + 17 r t - r w - 2 t w + 2 t^{2}$

Step 5

Move $17 r t$ .

$8 r^{2} - r w - 2 t w + 17 r t + 2 t^{2}$

Step 6

Move $8 r^{2}$ .

$- r w - 2 t w + 8 r^{2} + 17 r t + 2 t^{2}$