Multiply. (c^2 - d^2) \ast (c^2 - d^2)

Question:

Multiply.

{eq}\left(c^2 - d^2\right) \ast \left(c^2 - d^2\right) {/eq}

Distributive Property:

The distributive property helps to multiply a sum by multiplying each addend separately and then add the products. The given expression uses distributive property twice.

Distributive Property:

{eq}a(x+b)=ax+ab {/eq}.

They also make use of the properties of exponents.

  • If the base is same and in product the powers can be added.

Answer and Explanation:

{eq}\begin{align*} (c^2 - d^2) \ast (c^2 - d^2)&=c^2(c^2-d^2)-d^2(c^2-d^2)&\text{[Multiply using distributive property]}\\ &=(c^2)(c^2)-c^2d^2-d^2c^2-(-d^2d^2)&\text{[Multiply using distributive property]}\\ &=c^4-c^2d^2-c^2d^2+d^4&\text{[Evaluate using the properties of exponents]}\\ &=c^4+d^4-2c^2d^2&\text{[Simplify]} \end{align*} {/eq}


Learn more about this topic:

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Distributive Property: Definition, Use & Examples

from High School Algebra II: Help and Review

Chapter 2 / Lesson 20
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