Textbook Question
In Exercises 33–68, add or subtract as indicated. x/(x2−2x−24) − x/(x2−7x+6)
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0. Review of Algebra
Polynomials Intro
2:30 minutesProblem 45
Textbook Question
Find each product. (4x2-5y)(4x2+5y)
Verified step by step guidance1
Identify the expression to be multiplied: \((4x^2 - 5y)(4x^2 + 5y)\).
Recognize that this is a product of two binomials in the form \((a - b)(a + b)\), which is a difference of squares pattern.
Recall the difference of squares formula: \((a - b)(a + b) = a^2 - b^2\).
Apply the formula by letting \(a = 4x^2\) and \(b = 5y\), so the product becomes \((4x^2)^2 - (5y)^2\).
Square each term separately: \((4x^2)^2 = 16x^4\) and \((5y)^2 = 25y^2\), then write the final expression as \$16x^4 - 25y^2$.
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Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Polynomial Multiplication
Polynomial multiplication involves multiplying each term in one polynomial by every term in the other polynomial. This process requires applying the distributive property to combine like terms and simplify the expression.
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Difference of Squares
The difference of squares is a special product formula: (a - b)(a + b) = a^2 - b^2. Recognizing this pattern allows for quick multiplication and simplification of expressions that fit this form.
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Combining Like Terms
After multiplying polynomials, like terms (terms with the same variables and exponents) must be combined by adding or subtracting their coefficients to simplify the final expression.
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