Question

Dado os polinomios A=4x^3+5 e B=x^2-7 determine:
(A+B)^2=
A^2-B^2
A^2 B^2

Answer 1

Bom dia Maria 

A = 4x³ + 5
B = x² - 7 

A + B = 4x³ + x² - 2

(A + B)² = (4x³ + x² - 2)² = 16x⁶ + 8x⁵ + x⁴ - 16x³ - 4x² + 4

A² = (4x³ + 5)² = 16x⁶ + 40x³ + 25 
B² = (x² - 7)²  = x⁴ - 14x² + 49 

A² - B² = 16x⁶ + 40x³ + 25 - x⁴ + 14x² - 49 = 16x⁶ - x⁴ + 40x³ + 14x² - 24

A² * B² = (16x⁶ + 40x³ + 25 )*(x⁴ - 14x² + 49) = 
16x¹⁰-224x⁸+40x⁷+784x⁶-560x⁵+25x⁴+1960x³-350x²+1225

Answer 2

A=4x^3+5 e B=x^2-7 determine:


(A+B)^2=(4x^3+5+x^2-7)^2=>(4x^3+x^2-2)^2=> (4x^3+x^2-2)(4x^3+x^2-2)

16x^6 + 4x^5 - 8x^3 + 4x^4 + x^3 - 2x^2 - 8x^3 - 2x^2 + 4

16x^6 + 4x^5 + 4x^4 -15x^3 - 4x^2 + 4

A^2-B^2 = (4x^3+5)^2 - (x^2-7)^2 => 16x^6 +40x^3 + 25 -(x^4 - 14x^2 + 49)

16x^6 +40x^3 + 25 -x^4 + 14x^2 - 49 ==> 16x^6 - x^4 + 40x^3 + 14x^2 - 24
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A^2 + B^2 =  16x^6 +40x^3 + 25 + x^4 - 14x^2 + 49

16x^6 + x^4 +40x^3 - 14x^2 + 74