Expand (x + 7)(x − 2).

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Multiple Choice

Expand (x + 7)(x − 2).

Explanation:
Expanding two binomials uses the distributive property: multiply every term in the first binomial by every term in the second, then combine like terms. Multiply x by x to get x^2, x by -2 to get -2x, 7 by x to get 7x, and 7 by -2 to get -14. Now combine the like terms in the middle: -2x + 7x = 5x. So the result is x^2 + 5x - 14. You can check with the same approach by FOIL: First terms give x^2, Outer gives -2x, Inner gives 7x, Last gives -14; add them to get x^2 + 5x - 14. The coefficient of x must be 5, not 1, 9, or -5, and the constant term must be -14 because -2 times 7 is -14.

Expanding two binomials uses the distributive property: multiply every term in the first binomial by every term in the second, then combine like terms.

Multiply x by x to get x^2, x by -2 to get -2x, 7 by x to get 7x, and 7 by -2 to get -14. Now combine the like terms in the middle: -2x + 7x = 5x. So the result is x^2 + 5x - 14.

You can check with the same approach by FOIL: First terms give x^2, Outer gives -2x, Inner gives 7x, Last gives -14; add them to get x^2 + 5x - 14. The coefficient of x must be 5, not 1, 9, or -5, and the constant term must be -14 because -2 times 7 is -14.

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