Expand the expression to a polynomial in standard form:left bracket, 2, x, minus, 1, right bracket, left bracket, 2, x, squared, minus, x, plus, 7, right bracket(2x−1)(2x 2 −x+7)
Question
Expand the expression to a polynomial in standard form:left bracket, 2, x, minus, 1, right bracket, left bracket, 2, x, squared, minus, x, plus, 7, right bracket(2x−1)(2x 2 −x+7)
Solution
To expand the expression (2x - 1)(2x^2 - x + 7) to a polynomial in standard form, you need to distribute each term in the first bracket to each term in the second bracket.
First, distribute 2x to each term in the second bracket:
2x * 2x^2 = 4x^3 2x * -x = -2x^2 2x * 7 = 14x
Then, distribute -1 to each term in the second bracket:
-1 * 2x^2 = -2x^2 -1 * -x = x -1 * 7 = -7
Now, combine all the terms:
4x^3 - 2x^2 + 14x - 2x^2 + x - 7
Combine like terms:
4x^3 - 4x^2 + 15x - 7
So, the expression (2x - 1)(2x^2 - x + 7) expanded to a polynomial in standard form is 4x^3 - 4x^2 + 15x - 7.
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