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(3r-2t)⁴
I like the way your teacher showed you:
[(3r-2t)²]²
You need this two step rule for squaring any polynomial:
To square any polynomial, the two-step rule is
The sum of:
1. the squares of every term:
plus the sum of
2. Twice every product of every pair of terms.
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Let's do it this way:
[(3r-2t)²]²
Do the inside (3r-2t)² first by the two-step rule:
The sum of:
1. the squares of every term:
(3r)² + (-2t)² = 9r² + 4t²
plus
2. twice every product of every pair of terms.
(there's only one pair) 2(3r)(-2t) = -12rt
So [(3r-2t)²]² becomes
[9r² + 4t² - 12rt]²
Use the two-step rule again:
The sum of:
1. the squares of every term:
(9r²)² + (4t²)² + (-12rt)² = 81r⁴+ 16t⁴+ 144r²t²
plus the sum of
2. Twice every product of every pair of terms.
2(9r²)(4t²) + 2(9r²)(-12rt) + 2(4t²)(-12rt) =
72r²t² - 216r³t - 96rt³
So we have:
81r⁴+ 16t⁴+ 144r²t² + 72r²t² - 216r³t - 96rt³
The terms in r²t² combine and so the final answer is
81r⁴+ 16t⁴+ 216r²t² - 216r³t - 96rt³
Edwin
