Question

(a+2) (a^2-a-3); (a-2)*(a^2-a-3);

Answer 1

Ответ:

1)

(a+2)(a²-a-3)

a(a²-a-3)+2(a²-a-3)

a³-a²-3a+2a²-2a-6

a³+a²-5a-6

2)(a-2)*(a²-a-3)

a(a²-a-3)-2(a²-a-3)

a³-a²-3a-2a²+2a+6

a³-3a²-a+6

Answer 2

To expand the expressions (a+2)(a^2-a-3) and (a-2)(a^2-a-3), you can use the distributive property, also known as FOIL (First, Outer, Inner, Last). Here's how you can expand both expressions:

1. (a+2)(a^2-a-3):

First, distribute the (a+2) term to each term inside the parentheses:

(a+2)(a^2-a-3) = a(a^2-a-3) + 2(a^2-a-3)

Now, apply the distributive property to each term:

a(a^2) - a(a) - a(3) + 2(a^2) - 2(a) - 2(3)

Now, simplify each term:

a^3 - a^2 - 3a + 2a^2 - 2a - 6

Combine like terms:

a^3 + (2a^2 - a^2) + (-3a - 2a) - 6

a^3 + a^2 - 5a - 6

So, (a+2)(a^2-a-3) expands to a^3 + a^2 - 5a - 6.

2. (a-2)(a^2-a-3):

Similarly, distribute the (a-2) term to each term inside the parentheses:

(a-2)(a^2-a-3) = a(a^2-a-3) - 2(a^2-a-3)

Apply the distributive property:

a(a^2) - a(a) - a(3) - 2(a^2) + 2(a) + 2(3)

Simplify each term:

a^3 - a^2 - 3a - 2a^2 + 2a + 6

Combine like terms:

a^3 + (-a^2 - 2a^2) + (-3a + 2a) + 6

a^3 - 3a^2 - a + 6

So, (a-2)(a^2-a-3) expands to a^3 - 3a^2 - a + 6.