Evaluate 6a(3a^2b^2-7x^4y^5)

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Combine like terms for 6a(3a2b2 - 7x4y5)

We first need to simplify the expression removing parentheses
Simplify 6a(3a2b2 - 7x4y5): Distribute the 6a to each term in (3a^2b^2-7x^4y^5)
6a * 3a2b2 = (6 * 3)a(1 + 2)b2 = 18a3b2
6a * -7x4y5 = (6 * -7)ax4y5 = -42ax4y5
Our Total expanded term is 18a3b2-42ax4y5

Our updated term to work with is 18a3b2 - 42ax4y5

Evaluate the a3 terms:
18a3 ← There is only one a3 term

Evaluate the b2 terms:
b2 ← There is only one b2 term

Evaluate the ax4 terms:
-42ax4 ← There is only one ax4 term

Evaluate the y5 terms:
y5 ← There is only one y5 term

Combining all like terms, we get:
y5 - 42ax4 + 18a3 + b2

Analyze the 4 terms of the polynomial y5 - 42ax4 + 18a3 + b2

Analyze Term 1
Term 1 is y5
Since there is no coefficient before our variable, (term does not start with a number), our coefficient is 1
Our variable is the letter which is y
The exponent of our variable is the power that the variable is raised to which is 5
Analyze Term 2
Term 2 is -42a1
Our coefficient/constant is the number our term begins which is -42
Our variable is the letter which is a
The exponent of our variable is the power that the variable is raised to which is 1
Analyze Term 3
Term 3 is 18a3
Our coefficient/constant is the number our term begins which is 18
Our variable is the letter which is a
The exponent of our variable is the power that the variable is raised to which is 3
Analyze Term 4
Term 4 is b2
Since there is no coefficient before our variable, (term does not start with a number), our coefficient is 1
Our variable is the letter which is b
The exponent of our variable is the power that the variable is raised to which is 2
Determine the Degree of the Polynomial:
The degree of the polynomial (highest exponent) for the variable y = 5
The degree of the polynomial (highest exponent) for the variable a = 3
The degree of the polynomial (highest exponent) for the variable b = 2