Find the Product (-2d^2+s)(5d^2-6s)

$(- 2 d^{2} + s) (5 d^{2} - 6 s)$

Step 1

Expand $(- 2 d^{2} + s) (5 d^{2} - 6 s)$ using the FOIL Method.

Apply the distributive property.

$- 2 d^{2} (5 d^{2} - 6 s) + s (5 d^{2} - 6 s)$

Apply the distributive property.

$- 2 d^{2} (5 d^{2}) - 2 d^{2} (- 6 s) + s (5 d^{2} - 6 s)$

Apply the distributive property.

$- 2 d^{2} (5 d^{2}) - 2 d^{2} (- 6 s) + s (5 d^{2}) + s (- 6 s)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 2 \cdot 5 d^{2} d^{2} - 2 d^{2} (- 6 s) + s (5 d^{2}) + s (- 6 s)$

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

Move $d^{2}$ .

$- 2 \cdot 5 (d^{2} d^{2}) - 2 d^{2} (- 6 s) + s (5 d^{2}) + s (- 6 s)$

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

$- 2 \cdot 5 d^{2 + 2} - 2 d^{2} (- 6 s) + s (5 d^{2}) + s (- 6 s)$

Add $2$ and $2$ .

$- 2 \cdot 5 d^{4} - 2 d^{2} (- 6 s) + s (5 d^{2}) + s (- 6 s)$

Multiply $- 2$ by $5$ .

$- 10 d^{4} - 2 d^{2} (- 6 s) + s (5 d^{2}) + s (- 6 s)$

Rewrite using the commutative property of multiplication.

$- 10 d^{4} - 2 \cdot - 6 d^{2} s + s (5 d^{2}) + s (- 6 s)$

Multiply $- 2$ by $- 6$ .

$- 10 d^{4} + 12 d^{2} s + s (5 d^{2}) + s (- 6 s)$

Rewrite using the commutative property of multiplication.

$- 10 d^{4} + 12 d^{2} s + 5 s d^{2} + s (- 6 s)$

Rewrite using the commutative property of multiplication.

$- 10 d^{4} + 12 d^{2} s + 5 s d^{2} - 6 s \cdot s$

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

Move $s$ .

$- 10 d^{4} + 12 d^{2} s + 5 s d^{2} - 6 (s \cdot s)$

Multiply $s$ by $s$ .

$- 10 d^{4} + 12 d^{2} s + 5 s d^{2} - 6 s^{2}$

Add $12 d^{2} s$ and $5 s d^{2}$ .

Move $s$ .

$- 10 d^{4} + 12 d^{2} s + 5 d^{2} s - 6 s^{2}$

Add $12 d^{2} s$ and $5 d^{2} s$ .

$- 10 d^{4} + 17 d^{2} s - 6 s^{2}$