Textbook Question
In Exercises 33–68, add or subtract as indicated. 3/(2x+4) + 2/(3x+6)
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0. Review of Algebra
Polynomials Intro
2:42 minutesProblem 47
Textbook Question
Find each product. (4m+2n)2
Verified step by step guidance1
Recognize that the expression \( (4m + 2n)^2 \) is a binomial squared, which can be expanded using the formula for the square of a sum: \( (a + b)^2 = a^2 + 2ab + b^2 \).
Identify \( a = 4m \) and \( b = 2n \) in the expression \( (4m + 2n)^2 \).
Calculate \( a^2 \) by squaring \( 4m \), which means squaring both the coefficient and the variable: \( (4m)^2 = 4^2 \times m^2 \).
Calculate \( 2ab \) by multiplying 2, \( a = 4m \), and \( b = 2n \): \( 2 \times 4m \times 2n \).
Calculate \( b^2 \) by squaring \( 2n \): \( (2n)^2 = 2^2 \times n^2 \), then combine all parts to write the expanded form: \( a^2 + 2ab + b^2 \).
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Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Binomial Square Formula
The binomial square formula states that (a + b)^2 = a^2 + 2ab + b^2. It is used to expand the square of a sum of two terms by squaring each term and adding twice their product.
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Distributive Property
The distributive property allows multiplication over addition, meaning a(b + c) = ab + ac. This property is essential when expanding expressions like (4m + 2n)^2 by distributing each term properly.
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Combining Like Terms
After expanding an expression, like terms (terms with the same variable and exponent) must be combined to simplify the result. This step ensures the final expression is in its simplest form.
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