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29 tháng 7 2019

\(\left(a^2+4b^2-5\right)^2-16\left(ab+1\right)^2\)

\(=\left(a^2+4b^2-5\right)^2-4^2\left(ab+1\right)^2\)

\(=\left(a^2+4b^2-5\right)^2-\left[4\left(ab+1\right)\right]^2\)

\(=\left(a^2+4b^2-5\right)^2-\left[4ab+4\right]^2\)

\(=\left(a^2+4b^2-5-4ab-4\right)\left(a^2+4b^2-5+4ab+4\right)\)

\(=\left(a^2+4b^2-4ab-9\right)\left(a^2+4b^2+4ab-1\right)\)

29 tháng 7 2019

\(\left(a^2+4b^2-5\right)^2-16\left(ab+1\right)^2\)

\(\left(a^2+4b^2-5\right)^2-\left[4\left(ab+1\right)\right]^2\)

\(\left(a^2+4b^2-5\right)^2-\left(4ab+4\right)^2\)

\(\left(a^2+4b^2-5-4ab-4\right)\left(a^2+4b^2-5+4ab+4\right)\)

\(\left(a^2+4b^2-4ab-9\right)\left(a^2+4b^2+4ab-1\right)\)

\(\left[\left(a-2b\right)^2-3^2\right]\left[\left(a+2b\right)^2-1^2\right]\)

\(\left(a-2b-3\right)\left(a-2b+3\right)\left(a+2b-1\right)\left(a+2b+1\right)\)

24 tháng 6 2016

a)a3+2a2-13a+10

Ta thấy a=1;a=2 là nghiệm của đa thức nên:

=(a-2)(a-1)(a+5)

b)(a2+4b2-5)2-16(ab+1)2

=(a2+4b2-5+4ab+4)(a2+4b2-5-4ab-4)

=[(a+2b)2-1][(a-2b)2-9]

=(a+2b+1)(a+2b-1)(a-2b+3)(a-2b-3)

23 tháng 9 2018

\(4b^2c^2-\left(b^2+c^2-a^2\right)^2\)

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

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

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

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

\(\left(a^2+b^2-5\right)^2-4\left(ab+2\right)^2\)

\(=\left(a^2+b^2-5-2ab-4\right)\left(a^2+b^2-5+2ab+4\right)\)

\(=\left[\left(a-b\right)^2-3^2\right].\left[\left(a+b\right)^2-1\right]\)

\(=\left(a-b-3\right)\left(a-b+3\right)\left(a+b-1\right)\left(a+b+1\right)\)

Tham khảo nhé~

26 tháng 6 2016

1) \(a^3+2a^2-13a+10=a^3-a^2+3a^2-3a-10a+10=\)

\(=a^2\left(a-1\right)+3a\left(a-1\right)-10\left(a-1\right)=\left(a-1\right)\left(a^2+3a-10\right)\)

\(=\left(a-1\right)\left(a^2-2a+5a-10\right)=\left(a-1\right)\left[a\left(a-2\right)+5\left(a-2\right)\right]=\)

\(=\left(a-1\right)\left(a-2\right)\left(a+5\right)\)

b) \(\left(a^2+4b^2-5\right)^2-16\left(ab+1\right)^2=\left(a^2+4b^2-5+4ab+4\right)\left(a^2+4b^2-5-4ab-4\right)\)

\(=\left(a^2+4ab+4b^2-1\right)\left(a^2-4ab+4b^2-9\right)=\left[\left(a+2b\right)^2-1\right]\left[\left(a-2b\right)^2-9\right]=\)

\(=\left(a+2b+1\right)\left(a+2b-1\right)\left(a-2b+3\right)\left(a-2b-3\right)\)

2) \(6a-5b=1\Rightarrow5b=6a-1\Rightarrow25b^2=36a^2-12a+1\)

\(\Rightarrow4a^2+25b^2=40a^2-12a+1=40\left(a^2-2\cdot a\cdot\frac{3}{20}+\left(\frac{3}{20}\right)^2\right)+1-\frac{9}{10}\)

\(=40\left(a-\frac{3}{20}\right)^2+\frac{1}{10}\)

Vậy GTNN của \(4a^2+25b^2\)= 1/10. Xảy ra khi a = 3/20 và b = -1/50.

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) \(\left(4x^2-3x-18\right)^2-\left(4x^2+3x\right)^2\)

\(=\left(4x^2-3x-18+4x^2+3x\right)\left(4x^2-3x-18-4x^2-3x\right)\)

\(=\left(8x^2-18\right)\left(-6x-18\right)\)

\(=\left[2\left(4x^2-9\right)\right]\left[-6\left(x+3\right)\right]\)

\(=12\left(2x+3\right)\left(2x-3\right)\left(x+3\right)\)

15 tháng 7 2015

a) 

(x-y+5)2-2.(x-y+5)+1

=(x-y+5-1)2

=(x-y+4)2

b)

(x2+4y2-5)2-16.(x2.y2+2xy+1)

=(x2+4y2-5)2-[4.(xy+1)]2

=(x2+4y2-5-4xy-4)(x2+4y2-5+4xy+4)

=(x2+4y2-4xy-9)(x2+4y2+4xy-1)

=[(x-2y)2-9][(x+2y)2-1]

=(x-2y-3)(x-2y+3)(x+2y-1)(x+2y+1)

=(x2+x-3x-3)((x-2y+3)(x+2y-1)(x+1)2

=[x(x+1)-3(x+1)](x-2y+3)(x+2y-1)(x+1)2

=(x+1)(x-3)(x-2y+3)(x+2y-1)(x+1)2

16 tháng 10 2020

(x - 5)2 - 4(x - 3)2 + 2(2x - 1)(x - 5) + (2x - 1)2

= [(x - 5)2 + 2(2x - 1)(x - 5) + (2x - 1)2) - [2(x - 3)]2

= (x - 5 + 2x - 1)2 - (2x - 6)2

= (3x - 6)2 - (2x - 6)2

= (3x - 6 - 2x + 6)(3x - 6 + 2x - 6) = x(5x - 12)

16 tháng 10 2020

( x - 5 )2 - 4( x - 3 )2 + 2( 2x - 1 )( x - 5 ) + ( 2x - 1 )2

= [ ( x - 5 )2 + 2( 2x - 1 )( x - 5 ) + ( 2x - 1 )2 ] - 22( x - 3 )2

= ( x - 5 + 2x - 1 )2 - ( 2x - 6 )2

= ( 3x - 6 )2 - ( 2x - 6 )2

= ( 3x - 6 - 2x + 6 )( 3x - 6 + 2x - 6 )

= x( 5x - 12 )

DD
19 tháng 6 2021

a) \(100x^2-\left(x^2+25\right)^2=\left(10x\right)^2-\left(x^2+25\right)^2=\left(10x-x^2-25\right)\left(10x+x^2+25\right)\)

\(=-\left(x-5\right)^2\left(x+5\right)^2\)

b) \(\left(x-y+5\right)^2-2\left(x-y+5\right)+1=\left(x-y+5-1\right)^2=\left(x-y+4\right)^2\)

c) \(\left(x^2+4y^2-5\right)^2-16\left(x^2+y^2+2xy+1\right)\)

Có lẽ bạn ghi sai đề rồi nha. 

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)