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# distributive property of multiplication problems

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Question:I'm doing my homework and i stumbled on a few questions that look like this.... 5(7-4), (6-2)8, etc... I'm supposed to "rewrite each expression using the distributive property, then simplify". I did some addition problems with this like 4(3+5). I multiply 4 by each number in the parentheses then add right? I got 12+20=32 for that problem. Is it right? And if so, do i do the same thing for subtraction problems except subtract it instead of adding? I know.... Pretty basic stuff but i wanna be sure.

Answers:you are right my friend In mathematics, and in particular in abstract algebra, distributivity is a property of binary operations that generalises the distributive law from elementary algebra. For example: 2 (1 + 3) = (2 1) + (2 3). In the left-hand side of the above equation, the 2 multiplies the sum of 1 and 3; on the right-hand side, it multiplies the 1 and the 3 individually, with the results added afterwards. Because these give the same final answer (8), we say that multiplication by 2 distributes over addition of 1 and 3. Since we could have put any real numbers in place of 2, 1, and 3 above, and still have obtained a true equation, we say that multiplication of real numbers distributes over addition of real numbers.

Question:

Answers:no. only multiplication over addition X + X = x(1+1) however 2+(x*x) does not equal (2+x)(2+x)

Question:Question 1 (Multiple Choice Worth 2 points) Simplify 6(2r 5) + 2r 4r 30 4r + 30 14 r 30 12 r 30 Question 2 (Multiple Choice Worth 1 points) Simplify (6p + 12) 6p 12 6p + 12 6p + 12 6p 12 Question 3: simplify 5x - 10 / 5 x 10 5x 2 x 2 x 5 Question 4 (Multiple Choice Worth 2 points) Identify which distributive property problem below would help you solve the following scenario: Your Math class has 32 students. You would like to treat the class to cookies. You would like each person to have 5 cookies. Which expression would be a quick way to figure out how many cookies you would need to bake? 5(32 + 2) 5(30 + 2) 5(32 2) 5(30 2) Question 5 (Multiple Choice Worth 1 points) Simplify 4(9y + 2) 36y + 16 36y + 2 36y + 8 36y + 6 Question 6 (Multiple Choice Worth 1 points) Simplify (g 16) g 16 g 4 g + 4 g + 16 Question 7 (Essay Worth 2 points) Prove, in complete sentences, whether the left expression is equal to the right expression and discuss which property applies. 2(x 3) 2x 6

Answers:the distributive law(property) states that a(b+c) = ab + ac 1) 14r - 30 2) -6p - 12 3) x - 2 4) 5(30 + 2) 5) 36y + 8 6) g - 16 7) the property is the distributive law of multiplication over addition. imagine the bracket is like a basket. 2(x-3) means you have two of these baskets each with an x and a -3. So if there are 2 of these then overall there are 2x's and 2 (-3)'s (ie: 2x and -6)