Simplify (3a)(5x^2+8a)

$(3 a) (5 x^{2} + 8 a)$

Simplify by multiplying through.

Apply the distributive property.

$3 a (5 x^{2}) + 3 a (8 a)$

Reorder.

Rewrite using the commutative property of multiplication.

$3 \cdot 5 a x^{2} + 3 a (8 a)$

Rewrite using the commutative property of multiplication.

$3 \cdot 5 a x^{2} + 3 \cdot 8 a \cdot a$

Simplify each term.

Multiply $3$ by $5$ .

$15 a x^{2} + 3 \cdot 8 a \cdot a$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$15 a x^{2} + 3 \cdot 8 (a \cdot a)$

Multiply $a$ by $a$ .

$15 a x^{2} + 3 \cdot 8 a^{2}$

Multiply $3$ by $8$ .

$15 a x^{2} + 24 a^{2}$