Question

A to the power of 4 by 4(a+3)² plus 81 minus 18a- squared by 4(a+3)²​

Answer 1

The solution too the expression is:

4a⁶ + 6a⁵ - 63a⁴ - 108a³ - 162a² + 81

How to expand quadratic equations?

The quadratic expression can be expressed as:

a⁴ * 4(a + 3)² + 81 - 18a² * 4(a + 3)²

Expanding the bracket gives:

a⁴ * 4(a² + 6a + 9) + 81 - 18a² * 4(a² + 6a + 9))

Multiplying out the brackets gives us:

4a⁶ + 6a⁵ + 9a⁴ + 81 - 72a⁴ - 108a³ - 162a²

Rearranging in descending order of powers gives:

4a⁶ + 6a⁵ + 9a⁴ - 72a⁴ - 108a³ - 162a² + 81

= 4a⁶ + 6a⁵ - 63a⁴ - 108a³ - 162a² + 81

Complete question is:

Simplify the expression:

a to the power of 4 by 4(a+3)² plus 81 minus 18a- squared by 4(a+3)²​

Answer 2

The expression, a⁴ + 4(a + 3)² + 81 - 18a - 4(a + 3)² , when simplified is a⁴ - 18a + 81.

How do we simplify the expression?

First, we will expand the squares, then distribute the terms, and finally combine the like terms to simplify the given expression:

a⁴ + 4(a + 3)² + 81 - 18a - 4(a + 3)²

First, we expand the squares:

a⁴ + 4(a + 3)(a + 3) + 81 - 18a - 4(a + 3)²

Next, we distribute the terms:

a⁴ + 4(a² + 3a + 3(a + 3) + 81 - 18a - 4(a + 3)²

= a⁴ + 4(a² + 3a + 3a + 9) + 81 - 18a - 4(a + 3)²

Next, combine like terms:

a⁴ + 4 (a² + 6a + 9) + 81 - 18a - 4(a + 3)²

Distribute the terms:

a⁴ + 4a² + 24a + 36 + 81 - 18a - 4(a + 3)²

Then, expand the square:

a⁴ + 4a² + 24a + 36 + 81 - 18a - 4(a + 3)(a + 3)

And, distribute the terms:

a⁴ + 4a² + 24a + 36 + 81 - 18a - 4(a²+ 3a + 3(a + 3)

= a⁴ + 4a² + 24a + 36 + 81 - 18a - 4(a² + 3a + 3a + 9)

= a⁴ + 4a² + 24a + 36 + 81 - 18a - 4(a² + 6a + 9)

Next, combine like terms:

a⁴ + 4a² + 24a + 36 + 81 - 18a - 4a² - 24a - 36

Then, add the numbers:

a⁴ + 4a² + 24a + 81 - 18a - 4a² - 24a

Lastly, combine like terms:

a⁴ + 4a² - 18a - 4a² + 81

= a⁴ - 18a + 81

So, after simplifying the expression, a⁴ + 4(a + 3)² + 81 - 18a - 4(a + 3)², we have: a⁴ - 18a + 81.