Question

Dùng hằng đẳng thức để rút gọn:

a. (y-3)(y+3)(y^2+9)-(y^2+2)(y^2-2)

b. (a+b-c)^-(a-c)^2-2ab+2ab

c. (3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)

Answer 1

a)\(=\left(y^2-9\right)\left(y^2+9\right)-\left(y^4-4\right)=y^4-81-y^4+4=-77\)

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

Sửa lại đề bạn nhé! 

c) \(P\left(3-1\right)=\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(2P=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(2P=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

...

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

Answer 2

a,

(y-3)(y+3)-(y²+2)(y²-2)

=y²-9-y⁴-4

=y²-y⁴-9-4

=y²-y⁴-13

b,

đề ghi thiếu chỗ mũ rồi

c,

(3+1)(3²+1)(3⁴+1)(3⁸+1)(3¹⁶+1)(3³²+1)

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