Simplify (3x+7)*8x^2

$(3 x + 7) \cdot 8 x^{2}$

Simplify by multiplying through.

Apply the distributive property.

$3 x (8 x^{2}) + 7 (8 x^{2})$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$3 \cdot 8 x \cdot x^{2} + 7 (8 x^{2})$

Multiply $8$ by $7$ .

$3 \cdot 8 x \cdot x^{2} + 56 x^{2}$

Simplify each term.

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

Move $x^{2}$ .

$3 \cdot 8 (x^{2} x) + 56 x^{2}$

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

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

$3 \cdot 8 (x^{2} x^{1}) + 56 x^{2}$

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

$3 \cdot 8 x^{2 + 1} + 56 x^{2}$

Add $2$ and $1$ .

$3 \cdot 8 x^{3} + 56 x^{2}$

Multiply $3$ by $8$ .

$24 x^{3} + 56 x^{2}$