Question

Factor completely 81-4x^2 Please help me..

Answer 1

Answer:

(9-2x)(9+2x)

Step-by-step explanation:

81-4x^2=

9^2 - (2x)^2 =(*)

(9-2x)(9+2x)

(*) (A+B)(A-B)=A^2 - B^2

Answer 2

Answer: (9+2x)(9-2x)

Explanation: Here, you might need some of formulas.

$(x+y)^2=x^2+2xy+y^2\\(x-y)^2=x^2-2xy+y^2\\x^2-y^2=(x+y)(x-y)\\x^3+y^3=(x+y)(x^2-xy+y^2)\\x^3-y^3=(x-y)(x^2+xy+y^2)$

There are actually more but these formulas are common. You might need to memorize since you need it to solve the Quadratic Equation (Unless if you don't want to memorize these, you can memorize the Quadratic Formula which is kind of long.)

So from $81-4x^2$, It matches the third formula (The difference of two squares)

or $x^2-y^2=(x+y)(x-y)$ So which two same numbers multiply each others and get 81? That's 9 right? Because 9*9 = 81 or we can say 9^2 = 81

Now for 4x^2, which same numbers multiply each others and get 4x^2?

2*2 or 2^2 = 4, right? For x, x*x or x^2 = x^2 right?

So, 2x*2x = 4x^2

Then use the formula (The Difference of Two Square) to factor.

$x^2-y^2=(x+y)(x-y)\\x=9, y=2x\\(9+2x)(9-2x) #$

Therefore, the answer is (9+2x)(9-2x) or (9-2x)(9+2x). You can swap.