Question

What is the product of (p + 5)(p - 2) ?

Answer 1

To find the product of the expression (p + 5)(p - 2), you can use the distributive property (FOIL method):

(p + 5)(p - 2) = p(p) + p(-2) + 5(p) + 5(-2)

Now, multiply each pair of terms:

p(p) = p^2

p(-2) = -2p

5(p) = 5p

5(-2) = -10

Now, combine the like terms:

p^2 - 2p + 5p - 10

Combine the -2p and 5p terms:

p^2 + 3p - 10

So, the product of (p + 5)(p - 2) is p^2 + 3p - 10.

Answer 2

`\sf p^2 + 3p - 10`

Explanation:

The product of (p + 5)(p - 2) is given by the distributive property:

The distributive property is a property of multiplication that states that the product of a number and a sum is equal to the sum of the products of the number and each of the addends.

In other words, if a is a number and b and c are any expressions, then

`\sf a(b + c) = ab + ac`

In this case:

Applying Distributive property:

`\sf (p + 5)(p - 2) = p(p - 2) + 5(p - 2)`

Expanding the product, we get:

`\sf p^2 - 2p + 5p - 10`

Combining like terms, we get the answer:

`\sf p^2 + 3p - 10`

Therefore, the product of (p + 5)(p - 2) is:

`\sf p^2 + 3p - 10`