Complete as igualdades:
a) (x-3y^4)^2=x^2+__________+9y^8
b) (7/6xy-12)^2=49/36x^2y^2-_______+______
c) (3/8p^3+1.5)*(3/8p^3-1.5)=_________-_______
PFVR
Soluções para a tarefa
Complete as igualdades:
a) (x-3y^4)^2=x^2+__________+9y^8
(x - 3y⁴)² =
(x - 3y⁴)(x - 3y⁴) = passo a passo
x.x - x(3y⁴) - 3y⁴(x) + 3y⁴(3y⁴)
x² - 3xy⁴ - 3xy⁴ + 3.3y⁴y⁴
x² - 6xy⁴ + 9y⁸
assim
(x - 3y⁴)² = x² - 6xy⁴ + 9y⁸
b) (7/6xy-12)^2=49/36x^2y^2-_______+______
7
(------xy - 12)²
6
7xy 7xy
(------- - 12)(----------- - 12)
6 6
7xy(7xy) 7xy(12) 12(7xy)
------------- - ------------ - -------------- + 12.12
6.6 6 6
7.7xyxy 7(12)xy 12(7)xy
-------------- - ----------- - ------------ + 144
36 6 6
49xxyy 84xy 84xy
------------ - ------------- - ------------- + 144
36 6 6
49x²y²
------------- - 14xy - 14xy + 144
36
49x²y²
------------ - 28xy + 144 mesmo que
36
49/36x²y² - 28xy + 144
assim
(7/6xy - 12)² = 4936x²y² - 28xy + 144
c) (3/8p^3+1.5)*(3/8p^3-1.5)=_________-_______
3 3
(------p³ + 1.5)(-------p³ - 1.5) = mesmo que
8 8
3p³ 3p³
(-------- + 1.5)(-------- - 1.5)
8 8
3p³(3p³) 3p³(1.5) 1.5(3p³)
------------- - -------------- + ------------- - 1.5(1.5)
8.8 8 8
3.3p³p³ 0
------------ - 2.25
64 0
9p⁶
------ - 2.25 mesmo que
64
9/64p⁶ - 2.25
assim
(3/8p³ + 1.5)(3/8p³ - 1.5) = 9/64p⁶ - 2.25