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Đáp án:
$4)
a) x^3-16x^2+25x\\
b) a^2\\
c) 16\\
d) 2^{32}-1\\
e)
\dfrac{1}{2}.(3^{64}-1)\\
f)
-1\\
g) 2a^2-c^2\\
h)
x^6-64\\
6)
a)
M=1\\
b)
N=1\\
c)
A=-2\\
7)
A=4$
Giải thích các bước giải:
$4)
a) 2x(2x-1)^2-3x(x+3)(x-3)-4x(x+1)^2\\
=2x(4x^2-4x+1)-3x(x^2-9)-4x(x^2+2x+1)\\
=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x\\
=(8x^3-3x^3-4x^3)+(-8x^2-8x^2)+(2x+27x-4x)\\
=x^3-16x^2+25x\\
b) (a-b+c)^2-(b-c)^2+2ab-2ac\\
=a^2-2a.(b-c)+(b-c)^2-(b-c)^2+2ab-2ac\\
=a^2-2ab+2ac+2ab-2ac\\
=a^2\\
c) (3x+1)^2-2(3x+1)(3x+5)+(3x+5)^2\\
=(3x+1-3x-5)^2\\
=(-4)^2=16\\
d) (2+1)(2^2+1)(2^4+1)(2^8+1)(2^{16}+1)\\
=3.(2^2+1)(2^4+1)(2^8+1)(2^{16}+1)\\
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^{16}+1)\\
=(2^4-1)(2^4+1)(2^8+1)(2^{16}+1)\\
=(2^8-1)(2^8+1)(2^{16}+1)\\
=(2^{16}-1)(2^{16}+1)\\
=2^{32}-1\\
e)
(3+1)(3^2+1)(3^4+1)(3^8+1)(3^{16}+1)(3^{32}+1)\\
=\dfrac{1}{2}.2.4.(3^2+1)(3^4+1)(3^8+1)(3^{16}+1)(3^{32}+1)\\
=\dfrac{1}{2}.(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^{16}+1)(3^{32}+1)\\
=\dfrac{1}{2}.(3^4-1)(3^4+1)(3^8+1)(3^{16}+1)(3^{32}+1)\\
=\dfrac{1}{2}.(3^8-1)(3^8+1)(3^{16}+1)(3^{32}+1)\\
=\dfrac{1}{2}.(3^{16}-1)(3^{16}+1)(3^{32}+1)\\
=\dfrac{1}{2}.(3^{32}-1)(3^{32}+1)\\
=\dfrac{1}{2}.(3^{64}-1)\\
f)
10(11+1)(11^2+1)(11^4+1)(11^8+1)(11^{16}+1)(11^{32}+1)-11^{64}\\
=(11-1)(11+1)(11^2+1)(11^4+1)(11^8+1)(11^{16}+1)(11^{32}+1)-11^{64}\\
=(11^2-1)(11^2+1)(11^4+1)(11^8+1)(11^{16}+1)(11^{32}+1)-11^{64}\\
=(11^4-1)(11^4+1)(11^8+1)(11^{16}+1)(11^{32}+1)-11^{64}\\
=(11^8-1)(11^8+1)(11^{16}+1)(11^{32}+1)-11^{64}\\
=(11^{16}-1)(11^{16}+1)(11^{32}+1)-11^{64}\\
=(11^{32}-1)(11^{32}+1)-11^{64}\\
=11^{64}-1-11^{64}\\
=-1\\
g) (a+b-c)^2+(a-b+c)^2-2(b-c)^2\\
=(a+b)^2-2(a+b).c+c^2+(a-b)^2+2.(a-b).c+c^2-2(b^2-2bc+c^2)\\
=a^2+2ab+b^2-2ac-2bc+a^2-2ab+b^2+2ac-2bc+c^2-2b^2+4bc-2c^2\\
=(a^2+a^2)+(2ab-2ab)+(b^2+b^2-2b^2)+(-2ac+2ac)+(-2bc-2bc+4bc)+(c^2-2c^2)\\
=2a^2-c^2\\
h)
(x-2)(x^2-2x+4)(x+2)(x^2+2x+4)\\
=(x^3-2^3)(x^3+2^3)\\
=(x^3)^2-8^2\\
=x^6-64\\
6)
a)
M=x^3+y^3+3xy\\
=(x+y)(x^2-xy+y^2)+3xy\\
=x^2-xy+y^2+3xy\\
=x^2+2xy+y^2\\
=(x+y)^2=1\\
b)
N=x^3-y^3-3xy\\
=(x-y)(x^2+xy+y^2)-3xy\\
=x^2+xy+y^2-3xy\\
=x^2-2xy+y^2\\
=(x-y)^2\\
=1\\
c)
A=x^2+2xy+y^2-4x-4y+1\\
=(x+y)^2-4(x+y)+1\\
=3^2-4.3+1\\
=9-12+1\\
=-2\\
7)
A=2(x^3-y^3)-3(x+y)^2\\
=2(x-y)(x^2+xy+y^2)-3(x^2+2xy+y^2)\\
=2.2(x^2+xy+y^2)-3(x^2+2xy+y^2)\\
=4x^2+4xy+4y^2-3x^2-6xy-3y^2\\
=x^2-2xy+y^2\\
=(x-y)^2\\
=2^2=4$
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Bảng tin
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làm giúp tui bài 5,8 đc ko v Tui đăng câu hỏi lên cho làm
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Được ko