Question

[dung tran]

Bài 209. Rút gọn các biểu thức sau:

a) A = (3x + 1)² - 2(3x + 1)(3x + 5) + (5x + 5)²;

b) B = (3 + 1)(3² + 1)(3⁴ + 1)(3⁸ + 1)(3¹⁸ + 1)(3³² + 1);

c) C = (a + b - c)² + (a - b + c)² - 2(b - c)²;

d) D = (a + b + c)² + (a - b - c)² + (b - c - a)²+ (c - b - a)²;              E = (a + b + c + d)² + (a + b - c - d)² + (a + c - b - d)² + (a + d - b - c)²;

g) G = (a + b + c)³ - (b + c - a)³ - (a + c - b)³ + (a + b - c)³;

h) H = (a + b)³ + (b + c)³ + (c + a)³ - 3(a + b)(b + c)(c + a).

Answer 1

[Nguyễn Huy Tú]

Bài 209 : đăng tách ra cho mn cùng làm nhé 

a,sửa đề :  \(A=\left(3x+1\right)^2-2\left(3x+1\right)\left(3x+5\right)+\left(3x+5\right)^2\)

\(=\left(3x+1-3x-5\right)^2=\left(-4\right)^2=16\)

b, \(B=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{32}+1\right)\)

\(2B=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{32}+1\right)=\left(3^{32}-1\right)\left(3^{32}+1\right)\)

\(2B=3^{64}-1\Rightarrow B=\frac{3^{64}-1}{2}\)

c, \(C=\left(a+b-c\right)^2+\left(a-b+c\right)^2-2\left(b-c\right)^2\)

\(=2\left(a-b+c\right)^2-2\left(b-c\right)^2=2\left[\left(a-b+c\right)^2-\left(b-c\right)^2\right]\)

\(=2\left(a-b+c-b+c\right)\left(a-b+c+b-c\right)=2a\left(a-2b+2c\right)\)