Math

QuestionExpand the expression: (2x + 1)(x² - 5x - 7) to standard polynomial form.

Studdy Solution

STEP 1

Assumptions1. We are given the expression (x+1)(x5x7)( x+1)\left(x^{}-5 x-7\right). We need to expand this expression to a polynomial in standard form.

STEP 2

To expand the expression, we distribute each term in the first parentheses with each term in the second parentheses.(2x+1)(x2)+(2x+1)(5x)+(2x+1)(7)(2x+1)(x^{2}) + (2x+1)(-5x) + (2x+1)(-7)

STEP 3

Now, we distribute each term in the first parentheses with each term in the second parentheses.
2xx2+1x22x5x15x2x7172x \cdot x^{2} +1 \cdot x^{2} -2x \cdot5x -1 \cdot5x -2x \cdot7 -1 \cdot7

STEP 4

implify the multiplication in each term.
2x3+x210x2x14x72x^{3} + x^{2} -10x^{2} -x -14x -7

STEP 5

Combine like terms.
2x39x219x72x^{3} -9x^{2} -19x -7The expression (2x+1)(x25x7)(2 x+1)\left(x^{2}-5 x-7\right) expands to 2x39x219x72x^{3} -9x^{2} -19x -7 in standard form.

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