Question

Escreva na forma mais simples as expressões

a) (3ײ-2×+9) - (3×-1).(×+4)

b) (×-4)² + 2(×+3)² - (×-5)²

Answer 1

Resposta:

Explicação passo-a-passo:

a)

= (3ײ-2×+9) - (3×-1).(×+4)

= 3ײ-2×+9 - [ (3×-1).(×+4)]

= 3ײ-2×+9 - [(3ײ + 12x - x - 4]

= 3x² - 2x + 9 - [3x² + 11x - 4]

= 3x² - 3x² - 2x - 11x + 9 + 4

= - 13x + 13

b)

= (×-4)² + 2(×+3)² - (×-5)²

= x² - 2.4.x + 16 + 2.(x² + 2.3.x + 9) - [x² - 2.5.x + 25]

= x²-8x+16+2.(x²+6x+9) - [x²-10x +25]

=x²-8x+16+2x²+12x+18-x²+10x-25

= x²+2x²-x²-8x+12x+10x+16+18-25

= 2x² + 14x + 9

Answer 2

Explicação passo-a-passo:

a)

$(3 {x}^{2} - 2x + 9) - (3x - 1).(x + 4) \\ (3 {x}^{2} - 2x + 9) - | 3 {x}^{2} + 12x - x - 4 | \\ 3 {x}^{2} - 2x + 9 - 3 {x}^{2} - 12x + x + 4 \\ 3 {x}^{2} - 3 {x}^{2} - 2x - 12x + x + 9 + 4 \\ - 13x + 13$

b)

$(x - 4)^{2} + 2(x + 3 {)}^{2} - (x - 5 {)}^{2} \\ (x - 4). (x - 4) + 2. |(x + 3).(x + 3)| - </strong><strong>|</strong><strong>(x - 5).(x - 5)</strong><strong>|</strong><strong> \\ {x}^{2} - 4x - 4x + 16 + 2. | {x}^{2} + 3x + 3x + 9| - </strong><strong>|</strong><strong>{x}^{2} - 5x - 5x + 25</strong><strong>|</strong><strong> \\ {x}^{2} - 8x + 16 + 2 {x}^{2} + 6x + 6x + </strong><strong>1</strong><strong>8</strong><strong> - </strong><strong>|</strong><strong>{x}^{2} - 10x + 25</strong><strong>|</strong><strong> \\ </strong><strong> {x}^{2} - 8x + 16 + 2 {x}^{2} + 6x + 6x + 18</strong><strong> </strong><strong>-</strong><strong> </strong><strong>{</strong><strong>x</strong><strong>}</strong><strong>^</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong> </strong><strong>+</strong><strong> </strong><strong>1</strong><strong>0</strong><strong>x</strong><strong> </strong><strong>-</strong><strong> </strong><strong>2</strong><strong>5</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> {x}^{2} + {2x}^{2} </strong><strong>-</strong><strong> {x}^{2} - 8x + 6x + 6x </strong><strong>+</strong><strong> 10x + 16 + </strong><strong>1</strong><strong>8</strong><strong> </strong><strong>-</strong><strong> 25 \\ </strong><strong>2</strong><strong> {x}^{2} </strong><strong>+</strong><strong> </strong><strong>1</strong><strong>4</strong><strong>x + </strong><strong>9</strong><strong>$