Question

(2x-2)^2-16; (4в-9)^2-(3в+8)^2.​

Answer 1

$1)\; \; (2x-2)^2-16=(2x-2)^2-4^2=(2x-2-4)(2x-2+4)=\\\\=(2x-6)(2x+2)=4\, (x-3)(x+1)\\\\\\2)\; \; (4b-9)^2-(3b+8)^2=(4b-9-3b-8)(4b-9+3b+8)=\\\\=(b-17)(7b-1)$

$\boxed {\; A^2-B^2=(A-B)(A+B)\; }$

Answer 2

Объяснение:

1) (2x - 2)² - 16 = 4x² - 8x + 4 -16 = 4x² - 8x -1 2

Делим на 4: x² - 2x - 3

По теореме Виета: x₁ = -1 и x₂ = 3.

2) (4b - 9)² - (3b + 8)² = 16b² - 72b + 81 - 9b² - 48b - 64 = 7b² - 120b - 17

D = 14400 + 476 = 14876

x₁,₂ = $\frac{120 +- \sqrt{14876} }{14} =$

x₁ = $\frac{120 + \sqrt{14876} }{14}$

x₂ = $\frac{120 - \sqrt{14876} }{14}$

Answer 3

Let's simplify the given expressions:

1. Expression: (2x - 2)^2 - 16

Expanding the square: (2x - 2)^2 = (2x - 2) * (2x - 2) = 4x^2 - 4x - 4x + 4 = 4x^2 - 8x + 4

Substituting this back into the original expression: (2x - 2)^2 - 16 = 4x^2 - 8x + 4 - 16 = 4x^2 - 8x - 12

So, the simplified form of the expression (2x - 2)^2 - 16 is 4x^2 - 8x - 12.

2. Expression: (4в - 9)^2 - (3в + 8)^2

Expanding the squares: (4в - 9)^2 = (4в - 9) * (4в - 9) = 16в^2 - 36в - 36в + 81 = 16в^2 - 72в + 81

(3в + 8)^2 = (3в + 8) * (3в + 8) = 9в^2 + 24в + 24в + 64 = 9в^2 + 48в + 64

Substituting these back into the original expression: (4в - 9)^2 - (3в + 8)^2 = (16в^2 - 72в + 81) - (9в^2 + 48в + 64) = 16в^2 - 72в + 81 - 9в^2 - 48в - 64 = 16в^2 - 9в^2 - 72в - 48в + 81 - 64 = 7в^2 - 120в + 17

So, the simplified form of the expression (4в - 9)^2 - (3в + 8)^2 is 7в^2 - 120в + 17.