Question

(а-5)^2 - 2(а-5)(а+5) + (а+5)^2, при а= -4/9

Answer 1

(а-5)^2 - 2(а-5)(а+5) + (а+5)^2
(a+b)^2=a^2+2ab+b^2
((a-5)-(a+5))^2=(-10)^2=100
при любом a

Answer 2

To calculate the expression (а-5)^2 - 2(а-5)(а+5) + (а+5)^2 when а = -4/9, we substitute -4/9 for а and perform the calculations step by step.

Let's begin:

Step 1: Substitute -4/9 for а in the expression:

((-4/9)-5)^2 - 2((-4/9)-5)((-4/9)+5) + ((-4/9)+5)^2

Step 2: Simplify each term:

((-4/9-45/9)^2) - 2((-4/9-45/9)(-4/9+45/9)) + ((-4/9+45/9)^2)

Step 3: Continue simplifying:

((-49/9)^2) - 2((-49/9)(41/9)) + ((41/9)^2)

Step 4: Simplify further:

((2401/81) - 2(((-49/9)(41/9)))) + ((1681/81)

Step 5: Calculate the multiplication inside the parentheses:

((2401/81) - 2((-2009/81))) + ((1681/81)

Step 6: Simplify the multiplication:

((2401/81) + (4018/81)) + ((1681/81)

Step 7: Add the fractions:

8419/81 + 1681/81

Step 8: Combine the fractions:

10100/81

Therefore, when а = -4/9, the expression (а-5)^2 - 2(а-5)(а+5) + (а+5)^2 evaluates to 10100/81.