Simplify the expression. 6 ( 2 a − b ) + 4 ( 3 a + 5 b ) 6(2a-b)+4(3a+5b)

we're asked to simplify the expression six times two A minus B plus four times three A plus five B. Jumping right into our steps here, we wanna go ahead and distribute any constants or variables into parentheses. So looking at my expression here, I have this six that needs to get distributed into this two a and negative b, as well as this four that needs to get distributed to three a plus five b. So doing this multiplication here, six times two a is going to give me a 12 a and then six times negative b will give me a negative six b. Then distributing this four, four times three a is gonna give me positive 12 a and then four times five B is going to give me a positive 20 B. So with those terms distributed, we can move on to step two, identifying our like terms, those with the same variable raised to the same exponent. Now my first term is 12 a and I see I have another 12 a later on in my expression. These both have the same variable of a and that a is raised to the same exponent of one that is implied when there is no exponent. Then I have this negative six b and I also have positive 20 b. These are again like terms with that variable b raised to the same exponent of one. So with my like terms identified, I can go ahead and group my like terms by writing them next to each other. So I have 12 a plus 12 a. And then for my b terms, negative six b plus 20 b, just writing those right next to each other. Now we can move on to our final step here, combining our like terms by adding or subtracting their coefficients. Starting with our a terms here, I have 12 a plus 12 a. 12 plus 12 gives me 24, so that's 24 a. Then I have negative six B plus 20 B combining those coefficients negative six plus 20 gives me positive 14. So that's positive 14 B and now I have my fully simplified algebraic expression. Let us know if you have questions, and I'll see you in the next one.

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Intermediate Algebra

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Multiple Choice

Simplify the expression.
$6 (2 a - b) + 4 (3 a + 5 b)$

$24 a minus b$

$24 a plus b$

$24 a plus 14 b$

$24 a minus 14 b$

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Verified step by step guidance

Identify the expression to simplify: \$6(2a - b) + 4(3a + 5b)$.

Apply the distributive property to each term: multiply 6 by each term inside the first parentheses and 4 by each term inside the second parentheses. This gives \$6 \times 2a$, $6 \times (-b)$, $4 \times 3a$, and $4 \times 5b$.

Write out the expanded terms: \$12a - 6b + 12a + 20b$.

Combine like terms by adding the coefficients of $a$ terms together and the coefficients of $b$ terms together: $(12a + 12a)$ and $(-6b + 20b)$.

Express the simplified form as a single expression with combined terms: \$24a + 14b$.

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Simplify the expression.6(2a−b)+4(3a+5b)6(2a-b)+4(3a+5b)

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Simplify the expression.
$6 (2 a - b) + 4 (3 a + 5 b)$