Expand the expression to a polynomial in standard form:left bracket, 3, x, plus, 4, right bracket, left bracket, x, squared, minus, 3, x, minus, 3, right bracket(3x+4)(x 2 −3x−3)
Question
Expand the expression to a polynomial in standard form:left bracket, 3, x, plus, 4, right bracket, left bracket, x, squared, minus, 3, x, minus, 3, right bracket(3x+4)(x 2 −3x−3)
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:
First, distribute 3x to each term in the second bracket: 3x * x^2 = 3x^3 3x * -3x = -9x^2 3x * -3 = -9x
Then, distribute 4 to each term in the second bracket: 4 * x^2 = 4x^2 4 * -3x = -12x 4 * -3 = -12
Now, add all the terms together: 3x^3 - 9x^2 - 9x + 4x^2 - 12x - 12
Combine like terms: 3x^3 - 5x^2 - 21x - 12
So, the expression (3x+4)(x^2−3x−3) expands to the polynomial 3x^3 - 5x^2 - 21x - 12 in standard form.
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