Simplify 7t(t-4)-2t(8t^2-4t+3)

$7 t (t - 4) - 2 t (8 t^{2} - 4 t + 3)$

Step 1

Simplify each term.

Apply the distributive property.

$7 t \cdot t + 7 t \cdot - 4 - 2 t (8 t^{2} - 4 t + 3)$

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

Move $t$ .

$7 (t \cdot t) + 7 t \cdot - 4 - 2 t (8 t^{2} - 4 t + 3)$

Multiply $t$ by $t$ .

$7 t^{2} + 7 t \cdot - 4 - 2 t (8 t^{2} - 4 t + 3)$

Multiply $- 4$ by $7$ .

$7 t^{2} - 28 t - 2 t (8 t^{2} - 4 t + 3)$

Apply the distributive property.

$7 t^{2} - 28 t - 2 t (8 t^{2}) - 2 t (- 4 t) - 2 t \cdot 3$

Simplify.

Rewrite using the commutative property of multiplication.

$7 t^{2} - 28 t - 2 \cdot 8 t \cdot t^{2} - 2 t (- 4 t) - 2 t \cdot 3$

Rewrite using the commutative property of multiplication.

$7 t^{2} - 28 t - 2 \cdot 8 t \cdot t^{2} - 2 \cdot - 4 t \cdot t - 2 t \cdot 3$

Multiply $3$ by $- 2$ .

$7 t^{2} - 28 t - 2 \cdot 8 t \cdot t^{2} - 2 \cdot - 4 t \cdot t - 6 t$

Simplify each term.

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

Move $t^{2}$ .

$7 t^{2} - 28 t - 2 \cdot 8 (t^{2} t) - 2 \cdot - 4 t \cdot t - 6 t$

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

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

$7 t^{2} - 28 t - 2 \cdot 8 (t^{2} t^{1}) - 2 \cdot - 4 t \cdot t - 6 t$

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

$7 t^{2} - 28 t - 2 \cdot 8 t^{2 + 1} - 2 \cdot - 4 t \cdot t - 6 t$

Add $2$ and $1$ .

$7 t^{2} - 28 t - 2 \cdot 8 t^{3} - 2 \cdot - 4 t \cdot t - 6 t$

Multiply $- 2$ by $8$ .

$7 t^{2} - 28 t - 16 t^{3} - 2 \cdot - 4 t \cdot t - 6 t$

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

Move $t$ .

$7 t^{2} - 28 t - 16 t^{3} - 2 \cdot - 4 (t \cdot t) - 6 t$

Multiply $t$ by $t$ .

$7 t^{2} - 28 t - 16 t^{3} - 2 \cdot - 4 t^{2} - 6 t$

Multiply $- 2$ by $- 4$ .

$7 t^{2} - 28 t - 16 t^{3} + 8 t^{2} - 6 t$

Step 2

Simplify by adding terms.

Add $7 t^{2}$ and $8 t^{2}$ .

$15 t^{2} - 28 t - 16 t^{3} - 6 t$

Subtract $6 t$ from $- 28 t$ .

$15 t^{2} - 16 t^{3} - 34 t$

Reorder $15 t^{2}$ and $- 16 t^{3}$ .

$- 16 t^{3} + 15 t^{2} - 34 t$

Simplify 7t(t-4)-2t(8t^2-4t+3)

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