Question

(a-5)(a-5)(a-5)(a-5)

Answer 1

(a-5)(a-5)(a-5)(a-5)=(a-5)^4

Answer 2

To simplify the expression (a-5)(a-5)(a-5)(a-5), you can use the property of exponents that states a^m * a^n = a^(m+n) to combine the powers of a. Let's go step by step:

Step 1: Expand the expression: (a-5)(a-5)(a-5)(a-5)

Step 2: Multiply the first two factors using the distributive property: (a-5)(a-5) = a * a + a * (-5) + (-5) * a + (-5) * (-5) = a^2 - 5a - 5a + 25 = a^2 - 10a + 25

Step 3: Multiply the result from Step 2 by the third factor: (a^2 - 10a + 25)(a-5)

Using the distributive property again: = a^2 * a - 10a * a + 25 * a - a^2 * 5 - 10a * (-5) + 25 * (-5) = a^3 - 10a^2 + 25a - 5a^2 + 50a - 125 = a^3 - 15a^2 + 75a - 125

Step 4: Multiply the result from Step 3 by the fourth factor: (a^3 - 15a^2 + 75a - 125)(a-5)

Using the distributive property again: = a^3 * a - 15a^2 * a + 75a * a - 125 * a - a^3 * 5 + 15a^2 * 5 - 75a * 5 + 125 * 5 = a^4 - 15a^3 + 75a^2 - 125a - 5a^3 + 75a^2 - 375a + 625 = a^4 - 20a^3 + 150a^2 - 500a + 625

So, (a-5)(a-5)(a-5)(a-5) simplifies to a^4 - 20a^3 + 150a^2 - 500a + 625.