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Thu gọn biểu thức : ( x+3 ) ^ 2 - 9 ( x - 1 ) ^ 2 - 9x + 1

User Guerdy
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1 Answer

16 votes
16 votes

Answer:

(-(8 x^2 - 15 x - 1))

Explanation:

Simplify the following:

(x + 3)^2 - 9 (x - 1)^2 - 9 x + 1

(x + 3) (x + 3) = (x) (x) + (x) (3) + (3) (x) + (3) (3) = x^2 + 3 x + 3 x + 9 = x^2 + 6 x + 9:

(x^2 + 6 x + 9) - 9 (x - 1)^2 - 9 x + 1

(x - 1) (x - 1) = (x) (x) + (x) (-1) + (-1) (x) + (-1) (-1) = x^2 - x - x + 1 = x^2 - 2 x + 1:

9 + 6 x + x^2 - 9(x^2 - 2 x + 1) - 9 x + 1

Grouping like terms, 9 + 6 x + x^2 - 9 (x^2 - 2 x + 1) - 9 x + 1 = -9 (x^2 - 2 x + 1) + x^2 + (6 x - 9 x) + (9 + 1):

-9 (x^2 - 2 x + 1) + x^2 + (6 x - 9 x) + (9 + 1)

6 x - 9 x = -3 x:

-9 (x^2 - 2 x + 1) + x^2 + -3 x + (9 + 1)

9 + 1 = 10:

-9 (x^2 - 2 x + 1) + x^2 - 3 x + 10

-9 (x^2 - 2 x + 1) = -9 x^2 + 18 x - 9:

(-9 x^2 + 18 x - 9) + x^2 - 3 x + 10

Grouping like terms, x^2 - 9 x^2 + 18 x - 3 x - 9 + 10 = (-9 x^2 + x^2) + (18 x - 3 x) + (-9 + 10):

((-9 x^2 + x^2) + (18 x - 3 x) + (-9 + 10))

x^2 - 9 x^2 = -8 x^2:

-8 x^2 + (18 x - 3 x) + (-9 + 10)

18 x - 3 x = 15 x:

-8 x^2 + 15 x + (-9 + 10)

10 - 9 = 1:

-8 x^2 + 15 x + 1

Factor -1 out of -8 x^2 + 15 x + 1:

Answer: (-(8 x^2 - 15 x - 1))

User Hidde
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