Expand the expression to a polynomial in standard form:left bracket, 2, x, plus, 1, right bracket, left bracket, minus, 3, x, squared, minus, x, plus, 9, right bracket(2x+1)(−3x 2 −x+9)
Question
Expand the expression to a polynomial in standard form:left bracket, 2, x, plus, 1, right bracket, left bracket, minus, 3, x, squared, minus, x, plus, 9, right bracket(2x+1)(−3x 2 −x+9)
Solution
To expand the expression to a polynomial in standard form, we need to distribute each term in the first bracket to each term in the second bracket.
Step 1: Distribute 2x to each term in the second bracket: 2x * -3x^2 = -6x^3 2x * -x = -2x^2 2x * 9 = 18x
Step 2: Distribute 1 to each term in the second bracket: 1 * -3x^2 = -3x^2 1 * -x = -x 1 * 9 = 9
Step 3: Combine like terms: -6x^3 - 2x^2 - 3x^2 - x + 18x + 9
Step 4: Simplify: -6x^3 - 5x^2 + 17x + 9
So, the expression (2x+1)(−3x^2 −x+9) expands to -6x^3 - 5x^2 + 17x + 9 in standard form.
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