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15 tháng 7 2018
a) \(4b^2c^2-\left(b^2+c^2-a^2\right)^2\)
\(=\left(2bc+b^2+c^2-a^2\right)\left(2bc-b^2-c^2+a^2\right)\)
\(=\left[\left(b+c\right)^2-a^2\right]\left[a^2-\left(b-c\right)^2\right]\)
\(=\left(b+c+a\right)\left(b+c-a\right)\left(a+b-c\right)\left(a-b+c\right)\)
b) \(\left(ax+by\right)^2-\left(ay+bx\right)^2\)
\(=\left(ax+by+ay+bx\right)\left(ax+by-ay-bx\right)\)
\(=\left(a+b\right)\left(x+y\right)\left(a-b\right)\left(x-y\right)\)
c) \(\left(a^2+b^2-5\right)^2-4\left(ab+2\right)^2\)
\(=\left(a^2+b^2-5+2ab+4\right)\left(a^2+b^2-5-2ab-4\right)\)
\(=\left[\left(a+b\right)^2-1\right]\left[\left(a-b\right)^2-9\right]\)
\(=\left(a+b+1\right)\left(a+b-1\right)\left(a-b+3\right)\left(a-b-3\right)\)
d) \(\left(4x^2-3x-18\right)^2-\left(4x^2+3x\right)^2\)
\(=\left(4x^2-3x-18+4x^2+3x\right)\left(4x^2-3x-18-4x^2-3x\right)\)
\(=\left(8x^2-18\right)\left(-6x-18\right)\)
\(=\left[2\left(4x^2-9\right)\right]\left[-6\left(x+3\right)\right]\)
\(=12\left(2x+3\right)\left(2x-3\right)\left(x+3\right)\)
PA
22 tháng 12 2016
\(\left(ax+by\right)^2-\left(ay+bx\right)^2\)
\(=\left(ax+by+ay+bx\right)\left(ax+by-ay-bx\right)\)
\(=\left[a\left(x+y\right)+b\left(x+y\right)\right]\left[a\left(x-y\right)-b\left(x-y\right)\right]\)
\(=\left(a+b\right)\left(a-b\right)\left(x+y\right)\left(x-y\right)\)
\(\left(a^2+b^2-5\right)^2-4\left(ab+2\right)^2\)
\(=\left[\left(a^2+b^2-5\right)+2\left(ab+2\right)\right]\left[\left(a^2+b^2-5\right)-2\left(ab+2\right)\right]\)
\(=\left[a^2+b^2-5+2ab+4\right]\left[a^2+b^2-5-2ab-4\right]\)
\(=\left[\left(a+b\right)^2-1\right]\left[\left(a-b\right)^2-9\right]\)
\(=\left(a+b-1\right)\left(a+b+1\right)\left(a-b-3\right)\left(a-b+3\right)\)
22 tháng 12 2016
a)
(ax+by)2 - (ay+bx)2
=(ax+by-ay-bx)(ax+by+ay+bx)
=[ a(x-y) -b(x-y)][ a(x+y) + b(x+y)]
=(a-b)(x-y)(a+b)(x+y)
b)(a2+b2-5)2 - 4(ab+2)2
=(a2+b2-5-2ab-4)(a2+b2-5+2ab+4)
=[ (a-b)2 -9][ (a+b)2 -1]
=(a-b-3)(a-b+3)(a+b-1)(a+b+1)
NT
2
22 tháng 7 2017
\(a^2-10a+25-4b^2\)
\(=\left(a^2-2.a.5+5^2\right)-\left(2b\right)^2\)
\(=\left(a-5\right)^2-\left(2b\right)^2\)
\(=\left(a-2b-5\right)\left(a+2b-5\right)\)
TN
20 tháng 7 2018
\(3ax-2bx-6ay+4by=\) \(\left(3ax-6ay\right)-\left(2bx-4by\right)\)
\(=3a\left(x-2y\right)-2b\left(x-2y\right)\)
\(=\left(3a-2b\right)\left(x-2y\right)\)
\(ma-mb+na-nb-pa+pb=\) \(m\left(a-b\right)+n\left(a-b\right)-p\left(a-b\right)\)
\(=\left(m+n-p\right)\left(a-b\right)\)
TM
3
19 tháng 7 2019
\(A=b^4-9a^2-4b^2+4=b^4-4b^2+4-9a^2\)
\(=\left(b^2-2\right)^2-9a^2\)
\(=\left(b^2-2+3a\right)\left(b^2-2-3a\right)\)
19 tháng 7 2019
\(A=b^4-9a^2-4b^2+4\)
\(A=\left(b^2\right)^2-2.2.b^2+2^2-9a^2\)
\(A=\left(b^2-2\right)^2-\left(3a\right)^2\)
\(A=\left(b^2-2-3a\right)\left(b^2-2+3a\right)\)
_Hắc phong_
3 tháng 8 2016
\(a^4+a^3+a^3b+a^2b\)
\(=a^2\left(a^2+a+b+b\right)\)
\(=a^2\left(a^2+a+2b\right)\)
\(a^3+4a^2+4a+3\)
3 tháng 8 2016
a, \(a^4+a^3+a^3b+a^2b=a^3\left(a+1\right)+a^2b\left(a+1\right)=\left(a+1\right)\left(a^2b+a^3\right)=a^2\left(a+1\right)\left(b+a\right)\)
9 tháng 8 2020
1) \(=5\left(x+y\right)-\left(x-y\right)\left(x+y\right)=\left(x+y\right)\left(5-x+y\right)\)
2) \(=3\left(x^2-4x+4\right)=3\left(x-2\right)^2\)
3) \(=\left(x^2-1\right)\left(x^2+1\right)=\left(x-1\right)\left(x+1\right)\left(x^2+1\right)\)
4) \(=\left(x-1\right)\left(x^4+x^3+x^2+x+1\right)\)
5) \(=3\left(a^2-10a+25-b^2\right)=3\left(\left(a-5\right)^2-b^2\right)=3\left(a-5-b\right)\left(a-5+b\right)\)
6) \(=a\left(x-y\right)\left(x+y\right)+b\left(x+y\right)=\left(x+y\right)\left(ax-ay+b\right)\)
\(ay^2-4ay+4a-by^2+4by-4b\)
\(=\left(ay^2-4ay+4a\right)-\left(by^2-4by+4b\right)\)
\(=a\left(y^2-4y+4\right)-b\left(y^2-4y+4\right)\)
\(=a\left(y-2\right)^2-b\left(y-2\right)^2\)
\(=\left(y-2\right)^2\left(a-b\right)\)
=(ay2-by2)+(-4ay+4by)+(4a-4b)
=y2(a-b)+ 4(a-b)
=(a-b)×(y2+4)