Expand the expression to a polynomial in standard form:left bracket, 4, x, minus, 1, right bracket, left bracket, minus, x, squared, plus, 6, x, plus, 9, right bracket(4x−1)(−x 2 +6x+9)
Question
Expand the expression to a polynomial in standard form:left bracket, 4, x, minus, 1, right bracket, left bracket, minus, x, squared, plus, 6, x, plus, 9, right bracket(4x−1)(−x 2 +6x+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 4x to each term in the second bracket: 4x * -x^2 = -4x^3 4x * 6x = 24x^2 4x * 9 = 36x
Step 2: Distribute -1 to each term in the second bracket: -1 * -x^2 = x^2 -1 * 6x = -6x -1 * 9 = -9
Step 3: Combine like terms: -4x^3 + 24x^2 + 36x + x^2 - 6x - 9
Step 4: Simplify: -4x^3 + 25x^2 + 30x - 9
So, the expression (4x−1)(−x^2 +6x+9) expands to -4x^3 + 25x^2 + 30x - 9 in standard form.
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