Expand and simplify the following expression: (ℎ+2)(ℎ−2)(h+2)(h−2)
Question
Expand and simplify the following expression: (ℎ+2)(ℎ−2)(h+2)(h−2)
Solution
Sure, let's expand and simplify the expression step by step.
Step 1: Expand the first two terms and the last two terms separately.
(ℎ+2)(ℎ−2) = h^2 - 4
(h+2)(h−2) = h^2 - 4
Step 2: Now multiply the results together.
(h^2 - 4)(h^2 - 4)
Step 3: Expand the above expression.
= h^4 - 4h^2 - 4h^2 + 16
Step 4: Combine like terms.
= h^4 - 8h^2 + 16
So, the simplified form of the expression (ℎ+2)(ℎ−2)(h+2)(h−2) is h^4 - 8h^2 + 16.
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