Expand the expression to a polynomial in standard form:left bracket, 2, x, minus, 3, right bracket, left bracket, 3, x, squared, minus, x, plus, 6, right bracket(2x−3)(3x 2 −x+6)
Question
Expand the expression to a polynomial in standard form:left bracket, 2, x, minus, 3, right bracket, left bracket, 3, x, squared, minus, x, plus, 6, right bracket(2x−3)(3x 2 −x+6)
Solution
To expand the expression to a polynomial in standard form, you need to distribute each term in the first bracket to each term in the second bracket. Here's how you do it:
Step 1: Multiply 2x by each term in the second bracket: 2x * 3x^2 = 6x^3 2x * -x = -2x^2 2x * 6 = 12x
Step 2: Multiply -3 by each term in the second bracket: -3 * 3x^2 = -9x^2 -3 * -x = 3x -3 * 6 = -18
Step 3: Combine like terms: 6x^3 - 2x^2 - 9x^2 + 12x + 3x - 18 = 6x^3 - 11x^2 + 15x - 18
So, the expression (2x−3)(3x^2−x+6) expands to 6x^3 - 11x^2 + 15x - 18 in standard form.
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