Simplify (3y^2)(4y^5)

Problem

(3*y2)*(4*y5)

Solution

1. Group the coefficients and the variables together using the associative and commutative properties of multiplication.

3⋅4⋅y2⋅y5

2. Multiply the numerical coefficients to find the new constant term.

3⋅4=12

3. Apply the product rule for exponents, which states that am⋅an=a(m+n) to combine the variable terms.

y2⋅y5=y(2+5)

4. Simplify the exponent by adding the powers together.

y(2+5)=y7

5. Combine the results to form the final simplified expression.

12*y7

Final Answer

(3*y2)*(4*y5)=12*y7

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