Questions: (y^2+6)(-2y^2+7)=

Solution Steps

To solve the expression \((y^{2}+6)(-2y^{2}+7)\), we need to apply the distributive property (also known as the FOIL method for binomials) to expand the product. This involves multiplying each term in the first binomial by each term in the second binomial and then combining like terms.

We start with the expression \((y^{2}+6)(-2y^{2}+7)\). To expand this, we apply the distributive property:

\[ (y^{2}+6)(-2y^{2}+7) = y^{2} \cdot (-2y^{2}) + y^{2} \cdot 7 + 6 \cdot (-2y^{2}) + 6 \cdot 7 \]

Calculating each term gives us:

• \(y^{2} \cdot (-2y^{2}) = -2y^{4}\)
• \(y^{2} \cdot 7 = 7y^{2}\)
• \(6 \cdot (-2y^{2}) = -12y^{2}\)
• \(6 \cdot 7 = 42\)

Now, we combine the like terms:

\[ -2y^{4} + (7y^{2} - 12y^{2}) + 42 = -2y^{4} - 5y^{2} + 42 \]

Final Answer