Binomial Theorem (Intro)

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Q1. What is the value of x in the equation 3(x + 2) = 2(x + 5)?

Solution:

Step 1: Distribute: 3x + 6 = 2x + 10. Step 2: Subtract 2x from both sides: x + 6 = 10. Step 3: Subtract 6 from both sides: x = 4.

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Q2. What is the value of x in the equation 4x + 5 = 2x + 17?

Solution:

Step 1: Subtract 2x from both sides: 2x + 5 = 17. Step 2: Subtract 5 from both sides: 2x = 12. Step 3: Divide by 2: x = 6.

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Q3. What is the factored form of x^2 + 7x + 10?

Solution:

Step 1: Find two numbers that multiply to 10 and add to 7: 5 and 2. Step 2: Write in factored form: (x + 5)(x + 2).

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Q4. What is the result of (x + 2)(x - 2)?

Solution:

Step 1: Recognize this as a difference of squares: (a + b)(a - b) = a^2 - b^2. Step 2: Here, a = x and b = 2. Result is x^2 - 4.