Question

1) (a+1) (a-1) (a^2+1) 2) (a/2 -5) (5+a/2)+ 25

Answer 1

Ответ:

внизу, вроде так

Объяснение:

1) (а+1)(а-1)(а^2+1) =( a^2 - 1 ) ( a^2 + 1 )= a^4+a^2-a^2-1

2) ( a/2 - 5 )(5 + a/2) + 25 = ( a/2 - 5 ) ( a/2 + 5 ) = ( a/2 )^2 - 5^2 =  a^2/2^2 - 25 = a^2/4 - 25

Answer 2

Let's simplify the given expressions:

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

Start by expanding the first two factors using the distributive property (FOIL):

(a+1)(a-1) = a(a) + a(-1) + 1(a) + 1(-1) = a^2 - a + a - 1 = a^2 - 1

Now, we have (a^2 - 1)(a^2 + 1). Notice that this is the difference of squares, so we can use the difference of squares formula: a^2 - b^2 = (a + b)(a - b).

In this case, a = a^2 and b = 1. So:

(a^2 - 1)(a^2 + 1) = (a + 1)(a - 1)(a^2 + 1)

So the simplified expression is (a + 1)(a - 1)(a^2 + 1).

2. (a/2 - 5)(5 + a/2) + 25:

First, let's expand the product of the first two terms:

(a/2 - 5)(5 + a/2) = (a/2 * 5) + (a/2 * a/2) - (5 * 5) - (5 * a/2)

Now, simplify each term:

(a/2 * 5) = 5a/2 (a/2 * a/2) = (a^2)/4 (5 * 5) = 25 (5 * a/2) = (5a)/2

Now, put it all together:

5a/2 + (a^2)/4 - 25 - (5a)/2

Notice that the (5a/2) and (-5a/2) terms cancel each other out:

(5a/2) - (5a/2) = 0

So, the simplified expression is:

(a^2)/4 - 25

Therefore, the simplified expression for (a/2 - 5)(5 + a/2) + 25 is (a^2)/4 - 25.