I need help with these please math?

Question

solve..

36a^2 - 25 = 0

a =

(x^7 - x^4)(x^7 + x^4)

I am trying really hard to learn these but so confuse... Please help and explain...

Answer 1

Good question!

36a^2 - 25 = 0 (difference of two squares: a^2 - b^2 = (a + b)(a - b))

(6a + 5)(6a - 5) = 0 (zero-product property)

6a + 5 = 0 or 6a - 5 = 0

6a = -5 or 6a = 5

a = -5/6 or a = 5/6 <===ANSWER

(x^7 - x^4)(x^7 + x^4) (FOIL: First, Outside, Inside, Last; remember when exponents are multiplied, you add them)

F = First = x^7 * x^7 = x^14

O = Outside = x^7 * x^4 = x^11

I = Inside = -x^4 * x^7 = -x^11

L = Last = -x^4 * x^4 = -x^8

x^14 + x^11 - x^11 - x^8 (combine like terms; you cannot add or subtract exponents if they do not have the same power)

x^14 - x^8 <===Answer

*Hope this helped!!*

-Marissa,C <33

Answer 2

36a^2 - 25 = 0  (add 25 to both sides)

36a^2 = 25  (take square root of both sides)

6a = 5  or  6a = -5  (divide both sides by 6)

a = 5/6 or a = -5/6  <-- There's your answer.

With that second one, are you supposed to simplify?

Use F.O.I.L. (first, outer, inner, last)

(x^7 - x^4)(x^7 + x^4)

first: x^7 * x^7 = x^14

outer: x^7 * x^4 = x^11

inner: -x^4 * x^7 = -x^11

last: -x^4 * x^4 = -x^8

x^14 + x^11 - x^11 - x^8  (x^11 cancels)

x^14 - x^8  <-- Answer

Answer 3

36a^2 - 25 = 0 (difference of two squares: a^2 - b^2 = (a + b)(a - b))

(6a + 5)(6a - 5) = 0 (zero-product property)

6a + 5 = 0 or 6a - 5 = 0

6a = -5 or 6a = 5

a = -5/6 or a = 5/6 <===ANSWER

(x^7 - x^4)(x^7 + x^4) (FOIL: First, Outside, Inside, Last; remember when exponents are multiplied, you add them)

F = First = x^7 * x^7 = x^14

O = Outside = x^7 * x^4 = x^11

I = Inside = -x^4 * x^7 = -x^11

L = Last = -x^4 * x^4 = -x^8

x^14 + x^11 - x^11 - x^8 (combine like terms; you cannot add or subtract exponents if they do not have the same power)

x^14 - x^8 <===ANSWER