Write in Standard Form (y^2+6)(-2y^2+7)

$(y^{2} + 6) (- 2 y^{2} + 7)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Expand $(y^{2} + 6) (- 2 y^{2} + 7)$ using the FOIL Method.

Apply the distributive property.

$y^{2} (- 2 y^{2} + 7) + 6 (- 2 y^{2} + 7)$

Apply the distributive property.

$y^{2} (- 2 y^{2}) + y^{2} \cdot 7 + 6 (- 2 y^{2} + 7)$

Apply the distributive property.

$y^{2} (- 2 y^{2}) + y^{2} \cdot 7 + 6 (- 2 y^{2}) + 6 \cdot 7$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 2 y^{2} y^{2} + y^{2} \cdot 7 + 6 (- 2 y^{2}) + 6 \cdot 7$

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

Move $y^{2}$ .

$- 2 (y^{2} y^{2}) + y^{2} \cdot 7 + 6 (- 2 y^{2}) + 6 \cdot 7$

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

$- 2 y^{2 + 2} + y^{2} \cdot 7 + 6 (- 2 y^{2}) + 6 \cdot 7$

Add $2$ and $2$ .

$- 2 y^{4} + y^{2} \cdot 7 + 6 (- 2 y^{2}) + 6 \cdot 7$

Move $7$ to the left of $y^{2}$ .

$- 2 y^{4} + 7 \cdot y^{2} + 6 (- 2 y^{2}) + 6 \cdot 7$

Multiply $- 2$ by $6$ .

$- 2 y^{4} + 7 y^{2} - 12 y^{2} + 6 \cdot 7$

Multiply $6$ by $7$ .

$- 2 y^{4} + 7 y^{2} - 12 y^{2} + 42$

Subtract $12 y^{2}$ from $7 y^{2}$ .

$- 2 y^{4} - 5 y^{2} + 42$