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What is equivalent to (4x+7)(4x+7)(4x-7)(4x-7)

User ABrowne
by
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1 Answer

3 votes

Answer:

256 x^4 - 1568 x^2 + 2401 or (49 - 16 x^2)^2

Explanation:

Expand the following:

(4 x + 7) (4 x + 7) (4 x - 7) (4 x - 7)

(4 x + 7) (4 x + 7) (4 x - 7) (4 x - 7) = (4 x + 7)^2 (4 x - 7)^2:

(4 x + 7)^2 (4 x - 7)^2

(4 x - 7) (4 x - 7) = (4 x) (4 x) + (4 x) (-7) + (-7) (4 x) + (-7) (-7) = 16 x^2 - 28 x - 28 x + 49 = 16 x^2 - 56 x + 49:

(16 x^2 - 56 x + 49) (4 x + 7)^2

(4 x + 7) (4 x + 7) = (4 x) (4 x) + (4 x) (7) + (7) (4 x) + (7) (7) = 16 x^2 + 28 x + 28 x + 49 = 16 x^2 + 56 x + 49:

(16 x^2 + 56 x + 49) (16 x^2 - 56 x + 49)

| | | | 16 x^2 | + | 56 x | + | 49

| | | | 16 x^2 | - | 56 x | + | 49

| | | | 784 x^2 | + | 2744 x | + | 2401

| | -896 x^3 | - | 3136 x^2 | - | 2744 x | + | 0

256 x^4 | + | 896 x^3 | + | 784 x^2 | + | 0 | + | 0

256 x^4 | + | 0 | - | 1568 x^2 | + | 0 | + | 2401:

Answer: 256 x^4 - 1568 x^2 + 2401 or (49 - 16 x^2)^2

User Dahn
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