Factor the expression:
\[ 49p^2 - 84pq + 36q^2 \]
Answer (2)
You're in luck.
When faced with a monster like this, take some time to look it over. Notice that the first term is a square, the last term is a square, and the middle term is double the product of the square roots. Noticing this, you realize immediately that the whole thing is a perfect square, and you can write its equivalent by inspection:
49p² -84pq + 36q² = (7p - 6q)²
The expression 49 p 2 − 84 pq + 36 q 2 is a perfect square trinomial that can be factored as ( 7 p − 6 q ) 2 . To verify, we check that the middle term equals double the product of the square roots of the first and last terms. Thus, the factorization is accurate and straightforward.
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