Question

Descompuneți în factori. 4(x-2)²+20(x-2)+25-(x+1)²​

Answer 1

Explicație pas cu pas:

Formule:

• (a + b)² = a² + 2ab + b²
• a² - b² = (a - b) • (a + b)

4(x - 2)² + 20(x - 2) + 25 - (x + 1)² =

[2•(x - 2)]² +20•(x - 2) + 5² - (x + 1)² =

[2•(x - 2)]² + 2•5•2•(x - 2) + 5² - (x + 1)² =

[2•(x - 2) + 5]² - (x + 1)² =

(2x - 4 + 5)² - (x + 1)² =

(2x + 1)² - (x + 1)² =

[(2x + 1) - (x + 1)] • [(2x + 1) + (x + 1)] =

(2x + 1 - x -1) • (2x + 1 + x + 1) =

(2x - x)•(3x + 2) =

x•(3x + 2)

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