Expand the Expression: (x-3)(x-6) Using the Distributive Property

Question

Resolve -

(x3)(x6)= (x-3)(x-6)=

Video Solution

Step-by-Step Solution

To solve this problem, we will expand the expression (x3)(x6)(x-3)(x-6) using the distributive property, which involves the following steps:

  • Step 1: Multiply the first terms of each binomial
    (x)(x)=x2(x)(x) = x^2

  • Step 2: Multiply the outer terms of the binomials
    (x)(6)=6x(x)(-6) = -6x

  • Step 3: Multiply the inner terms of the binomials
    (3)(x)=3x(-3)(x) = -3x

  • Step 4: Multiply the last terms of each binomial
    (3)(6)=18(-3)(-6) = 18

  • Step 5: Combine all the products
    x26x3x+18x^2 - 6x - 3x + 18

  • Step 6: Combine like terms
    6x3x=9x-6x - 3x = -9x, so we have
    x29x+18x^2 - 9x + 18

Therefore, the expanded form of (x3)(x6)(x-3)(x-6) is x29x+18\boxed{x^2 - 9x + 18}.

Therefore, the solution to the problem is x29x+18x^2 - 9x + 18. This corresponds to choice 1.

Answer

x29x+18 x^2-9x+18