Question

85- Escreva cada expressão por meio de um polinômio na forma reduzida:

a)
${(a + 1)}^{2} + {(2a)}^{3}$

b)
${(2a + b)}^{2} - {(a - b)}^{2}$

c)
$5 \times {( - a - b)}^{2} {(b + 3a)}^{2}$

d)
${( - a - b)}^{2} - 8ab - {a}^{2}$

e)
$(3a + 6b) \times (2a - 2) - {8a}^{2}$

f)
${( {a}^{3} - {b}^{2} ) }^{2} - 2 \times ( {b}^{4} - {a}^{6} ) + {2a}^{3} {b}^{2}$

g)
${(a + \frac{b}{2}) }^{2} \times + ( \frac{b}{2} - 5a) \times ( \frac{b}{2} + 5a)$
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Answer 1

Resposta:

a) (a+1)^2 + (2a)^3

a^2+2a+1+8a^3

8a^3+a^2+2a+1

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b) (2a+b)^2-(a-b)^2

4a^2 + 4ab+b^2-(a^2-2ab+b^2)

4a^2 +4ab +b^2-a^2+2ab-b^2

3a^2+6ab

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c) 5*(-a-b)^2+(b+3a)^2

5*(a^2+2ab+b^2)+(b^2+6ab+9a^2)

5a^2+10ab+5b^2+b^2+6ab +9a^2

14a^2+16ab 6b^2

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d) (-a-b)^2-8ab -a^2

a^2+2ab+b^2-8ab-a^2

-6ab+b^2

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e) (3a+6b)*(2a-2)-8a^2

6a^2-6a +6ab-12b-8a^2

-2a^2+6ab-6a-12b

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f) (a^3-b^2)^2-2*(b^4-a^6)+2a^3b^2

a^6-2a^3b^2+b^4-2b^4+2a^6.

2a^3b^2

3a^6 +b^4 -2b^4= 3a^6-b^4

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g)(a+b/2)^2 +(b/2-5a)*(b/2+5a)

a^2+2ab/2+ b^2/4+ b^2/4-25a^2

-24a^2+2b^2/4+2ab/2

-24a^2+2ab/2+2b^2/4