9m2−34mn+4n2=?
To solve this problem, we'll simplify the expression 9m2−34mn+4n2 to reveal a possible square of a binomial:
- Step 1: Recognize the expression 9m2−34mn+4n2 may have terms fitting the identity (a−b)2=a2−2ab+b2.
- Step 2: Identify parts of the expression:
- a2=9m2, so a=3m.
- −2ab=−34mn. Since a=3m, solve for b:
2×3m×b=34mn⇒2b=4n⇒b=2n.
- Step 3: Check b2: b2=(2n)2=4n2, which matches the 4n2 term in the expression.
Therefore, the correct form of the expression is:
(3m−2n)2.
Thus, the expression simplifies to:
(3m−2n)2
(3m−2n)2