Combine Like Terms 3a-{4a+3[2a-2(2a+3b)-(a-b)-6(a+b)]-(7a-6b)}

Publish date: 2024-06-12
Combine Like Terms 3a-{4a+3[2a-2(2a+3b)-(a-b)-6(a+b)]-(7a-6b)} MathCelebrity logo Image to Crop

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Combine like terms for:

3a - {4a + 3[2a - 2(2a + 3b) - (a - b) - 6(a + b)] - (7a - 6b)}

Simplify by removing parentheses
Simplify -2(2a + 3b):
Distribute the -2 to each term in (2a+3b)
-2 * 2a = (-2 * 2)a = -4a
-2 * 3b = (-2 * 3)b = -6b
Our Total expanded term is -4a-6b

Simplify -(a - b):
Distribute the - to each term in (a-b)
- * a = (-1 * 1)a = -1a
- * -b = (-1 * -1)b = 1b
Our Total expanded term is -1a + 1b

Simplify -6(a + b):
Distribute the -6 to each term in (a+b)
-6 * a = (-6 * 1)a = -6a
-6 * b = (-6 * 1)b = -6b
Our Total expanded term is -6a-6b

Simplify -(7a - 6b):
Distribute the - to each term in (7a-6b)
- * 7a = (-1 * 7)a = -7a
- * -6b = (-1 * -6)b = 6b
Our Total expanded term is -7a + 6b

Our new term is
3a - {4a + 3[2a - 4a - 6b - 1a + 1b - 6a - 6b] - 7a + 6b}

Evaluate the a terms:

3a + 4a + 2a + - 4a + - 1a + - 6a + - 7a

(3 + 4 + 2 - 4 - 1 - 6 - 7)a

-9a

Evaluate the b terms:

-6b + 1b + - 6b + 6b

( - 6 + 1 - 6 + 6)b

-5b

Combine like terms

-9a - 5b

Analyze the 2 terms of the polynomial -9a - 5b

Analyze Term 1

Term 1 is -9a

Our coefficient/constant is -9
Our variable is the letter which is a
No exponent exists for this term

Analyze Term 2

Term 2 is -5b

Our coefficient/constant is -5
Our variable is the letter which is b
No exponent exists for this term

Determine the Degree of the Polynomial:

What is the Answer?

Our coefficient/constant is -9
Our variable is the letter which is a
No exponent exists for this term
Our coefficient/constant is -5
Our variable is the letter which is b
No exponent exists for this term

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constanta value that always assumes the same value independent of how its parameters are variedexponentThe power to raise a numberexpressionfinite combination of symbolspolynomialan expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).terma single number or variable, or numbers and variables multiplied togethervariableAlphabetic character representing a number

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