Rút gọn biểu thức:
P=12(52+1)(54+1)(58+1)(516+1)
\(P=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^{16}-1\right)\left(5^{16}+1\right)\)
\(2P=5^{32}-1\Rightarrow P=\dfrac{5^{32}-1}{2}\)
x^2-x = -2x+2
Phân tích các đa thức sau thành nhân tử:
\(l,x^4+x^2+1\)
\(m,\left(x^2-8\right)^2+36\)
\(n,4x^4+81\)
Chứng minh các đa thức sau luôn luôn âm với mọi x
a) \(-x^2+6x-15\)
b) \(\left(x-3\right).\left(1-x\right)-2\)
c) \(\left(x+4\right).\left(2-x\right)-10\)
\(f,x^2-6x+5\)
\(g,x^4+64\)
\(d,2x^2-3x-27\)
\(e,2x^2-5xy-3y^2\)
\(i,x^2+y^2-2xy-4x+4y\)
\(a,6x^2+11x+3\)
\(g,8x^3-27y^3\)
\(h,x^3+y^3+2x^2-2xy+2y^2\)
\(e,x^2-y^2+2x+1\)
\(f,x^3+2x^2+2x+1\)
\(c,\left(ab+1\right)^2-\left(a+b\right)^2\)
\(d,x^2-2x-4y^2-4y\)
\(a,\left(x+y\right)^3-x^3-y^3\)
\(b,x^2+6xy+9y^2\)
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