21. simplify (2sqrt5+3sqrt7)^2 show your work. Been confused on it for a while.

(2√5+3√7)^2

(2√5)^2 + 2(2√5)(3√7) + (3√7)^2
4*5 + 2*2*3*√35 + 9*7
...

i dont understand thus

then you do

20+12sqrt35+36
20+63+12sqrt35
83+12sqrt35

also try using FOIL
whats Foil?
The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial. Then Outer means multiply the outermost terms in the product."

Have a good day!

girl me neither lets try our best to survive LMFAO

To simplify the expression (2√5 + 3√7)^2, we need to expand it using the binomial square formula. This formula states that for any two terms, (a + b)^2 is equal to a^2 + 2ab + b^2.

Let's apply this formula to our expression:

(2√5 + 3√7)^2

Using the formula, we have:

(a + b)^2 = a^2 + 2ab + b^2

Here, a = 2√5 and b = 3√7.

Substituting these values into the formula, we get:

(2√5)^2 + 2 * (2√5) * (3√7) + (3√7)^2

Now simplify each term:

(2^2 * (√5)^2) + 2 * 2 * √5 * √7 + (3^2 * (√7)^2)

= 4 * 5 + 2 * 2 * √(5 * 7) + 9 * 7

= 20 + 4√(35) + 63

Combine like terms:

= 83 + 4√(35)

Therefore, (2√5 + 3√7)^2 simplifies to 83 + 4√35.