Simplify (x-7)( x+7)
You can multiply these binomials like any other.
x times x and x times 7
then -7 times x and - 7 times 7
x^2 + 7x - 7x -49
x^2 -49
Or you can recognize this pair as a sum and difference which always multiplies to be the difference of two squares.
(a+b)(a-b) = a^2 -b^2
To simplify the expression (x-7)(x+7), we'll use the distributive property. This property states that for any real numbers a, b, and c:
a(b + c) = ab + ac
So, applying the distributive property to the given expression, we have:
(x - 7)(x + 7) = x(x) + x(7) - 7(x) - 7(7)
Now we simplify each term:
x(x) = x^2 (using the exponent rule: x to the power of 1 multiplied by x to the power of 1 equals x to the power of 1+1, which is x^2)
x(7) = 7x
-7(x) = -7x
-7(7) = -49
Putting all the terms together, we have:
x^2 + 7x - 7x - 49
Notice that the 7x and -7x terms combine to give zero:
x^2 + 0 - 49
Therefore, the simplified form of (x-7)(x+7) is:
x^2 - 49