In solving the eqaution(x+4)(x-4),Eric stated thatthe solution would be x+4=33=>x=29

or
(x-4)=33=>x=37
However, at least one of these solutions fails to work when substituted back into the original eqaution. Why is that?Help Eric to understand better,solve the problem and explain your reasoning

(x+4)(x-4) is not an equation. An equation requires an equal sign (=).

I meant (x+4)(x-4)=33 thanks

To solve, it must = 0.

Does that help?

yes thanks

To solve the equation (x+4)(x-4), we can use the distributive property.

Expanding the equation, we get:

(x+4)(x-4) = x(x) + x(-4) + 4(x) + 4(-4) = x^2 - 4x + 4x - 16 = x^2 - 16

Now, let's solve for x by setting the equation equal to zero:

x^2 - 16 = 0

To find the solutions, we can apply factoring:

(x+4)(x-4) = 0

Setting each factor equal to zero:

x+4 = 0, which gives x = -4

x-4 = 0, which gives x = 4

So the solutions to the equation (x+4)(x-4) = 0 are x = -4 and x = 4.

Now let's check these solutions by substituting them back into the original equation:

For x = -4:
(x + 4)(x - 4) = (-4 + 4)(-4 - 4) = 0(8) = 0

For x = 4:
(x + 4)(x - 4) = (4 + 4)(4 - 4) = 8(0) = 0

Both of these solutions yield a result of 0, which confirms they are correct.

Therefore, the correct solutions to the equation (x+4)(x-4) = 0 are x = -4 and x = 4.

The mistake that Eric made was in setting each factor equal to 33, which led to incorrect solutions. It's important to set each factor equal to zero in order to find the correct solutions.