Which expression is equivalent to (z+4)(z−4)?(1 point)
Responses
2z2−z2−8
2 z squared minus z squared minus 8
z2−8z−16
z squared minus 8 z minus 16
z(z)+4z(z)−4(4)
z left parenthesis z right parenthesis plus 4 z left parenthesis z right parenthesis minus 4 left parenthesis 4 right parenthesis
z2+4z−4z−16
z squared plus 4z minus 4z minus 16
To expand the expression (z+4)(z-4), you can use the distributive property. The distributive property states that for any numbers a, b, and c, the product of a multiplied by the sum of b and c is equal to the sum of the products of a and b, and a and c.
In this case, we have (z+4)(z-4). To expand it, we will multiply each term in the first parentheses (z+4) by each term in the second parentheses (z-4):
(z+4)(z-4) = z(z) + z(-4) + 4(z) + 4(-4)
Now, simplify each term:
z(z) = z^2 (z squared, because z multiplied by z is z^2)
z(-4) = -4z (negative 4z, because z multiplied by -4 is -4z)
4(z) = 4z (4z, because z multiplied by 4 is 4z)
4(-4) = -16 (negative 16, because 4 multiplied by -4 is -16)
Now, combine the simplified terms:
z^2 - 4z + 4z - 16
-4z + 4z simplifies to 0:
z^2 - 16
Therefore, the expression (z+4)(z-4) is equivalent to z^2 - 16.