Simplify

Problem

(2√(,3*m)+3√(,5*n))*(2√(,3*m)−3√(,5*n))

Solution

1. Identify the pattern as a difference of squares, which follows the algebraic identity (a+b)*(a−b)=a2−b2

2. Assign the values for the variables in the identity where a=2√(,3*m) and b=3√(,5*n)

3. Apply the formula by squaring each term separately.

a2=(2√(,3*m))2

b2=(3√(,5*n))2

4. Simplify the squared terms by distributing the exponent to both the coefficient and the radicand.

(2√(,3*m))2=4*(3*m)=12*m

(3√(,5*n))2=9*(5*n)=45*n

5. Subtract the results to find the final simplified expression.

12*m−45*n

Final Answer

(2√(,3*m)+3√(,5*n))*(2√(,3*m)−3√(,5*n))=12*m−45*n

Want more problems? Check here!