Math Problem Statement

(8x-w)(x-3w)

Solution

To simplify the expression (8xw)(x3w)(8x - w)(x - 3w), let's expand it using the distributive property (also known as the FOIL method for binomials):

(8xw)(x3w)=8xx+8x(3w)wxw(3w)(8x - w)(x - 3w) = 8x \cdot x + 8x \cdot (-3w) - w \cdot x - w \cdot (-3w)

Now, let’s calculate each term separately:

  1. 8xx=8x28x \cdot x = 8x^2
  2. 8x(3w)=24xw8x \cdot (-3w) = -24xw
  3. wx=wx-w \cdot x = -wx
  4. w(3w)=3w2-w \cdot (-3w) = 3w^2

Combining all these terms, we get:

8x224xwwx+3w28x^2 - 24xw - wx + 3w^2

Now, we can combine like terms (24xwwx-24xw - wx):

8x225xw+3w28x^2 - 25xw + 3w^2

Thus, the simplified expression is:

8x225xw+3w28x^2 - 25xw + 3w^2

Would you like further explanation or have any questions?


Here are five related questions to deepen your understanding:

  1. How would this expansion differ if we had (8x+w)(x3w)(8x + w)(x - 3w)?
  2. Can you factor the expression 8x225xw+3w28x^2 - 25xw + 3w^2 further?
  3. What is the effect of changing coefficients in the initial expression on the expanded result?
  4. How would you simplify (axbw)(x+cw)(ax - bw)(x + cw) with different variables?
  5. What are the steps to apply the distributive property with more than two terms?

Tip: When expanding binomials, always ensure each term from one binomial multiplies each term in the other binomial to cover all possible products.

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Expansion
Binomials

Formulas

Distributive Property: (a + b)(c + d) = ac + ad + bc + bd

Theorems

Distributive Property

Suitable Grade Level

Grades 8-10