Please show solution to simplifying this expression:
( 5z-2 )( 5z+2)
Thank you.
(5z-2)(5z+2) = 25z^2 +10z - 10z - 4 = 25z^2 - 4.
or (5z)^2 - 2^2 = 25z^2 - 4.
To simplify the expression (5z-2)(5z+2), we can use the distributive property. The distributive property states that when you multiply a term by a sum or difference of terms, you distribute the term to each term inside the parentheses.
In this case, we have two binomials: (5z-2) and (5z+2). To simplify, we will multiply each term in the first binomial by each term in the second binomial and combine like terms.
Here's how you can do it step by step:
Step 1: Multiply the first terms of each binomial.
5z * 5z = 25z^2
Step 2: Multiply the first term of the first binomial by the last term of the second binomial.
5z * 2 = 10z
Step 3: Multiply the last term of the first binomial by the first term of the second binomial.
-2 * 5z = -10z
Step 4: Multiply the last terms of each binomial.
-2 * 2 = -4
Step 5: Combine like terms.
10z + (-10z) simplifies to 0z (which is just 0, as any number multiplied by 0 is 0).
So, the simplified expression is: 25z^2 - 4
Therefore, (5z-2)(5z+2) simplifies to 25z^2 - 4.