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\(1,=a\left(x+y\right)+\left(x-y\right)\left(x+y\right)=\left(a+x-y\right)\left(x+y\right)\\ 2,=\left(x-2\right)\left(x+2\right)-y\left(x-2\right)=\left(x+2-y\right)\left(x-2\right)\\ 3,Sửa:x^2-2ax-2ay-y^2\\ =\left(x-y\right)\left(x+y\right)-2a\left(x+y\right)=\left(x-y-2a\right)\left(x+y\right)\)
a)\(ax+ay+x^2-y^2=a\left(x+y\right)+\left(x+y\right)\left(x-y\right)=\left(a+x-y\right)\left(x+y\right)\)
b)\(x^2-xy+2y-4=\left(x^2-4\right)-\left(xy-2y\right)=\left(x-2\right)\left(x+2\right)-y\left(x-2\right)=\left(x-2\right)\left(x+2-y\right)\)
c)\(x^2-2ax-4ay-y^2=\left(x^2-y^2\right)-\left(2ax+4ay\right)=\left(x-y\right)\left(x+y\right)-2a\left(x+y\right)=\left(x+y\right)\left(x-y-2a\right)\)
\(=x^2\left(a+b\right)-6x\left(a+b\right)+9\left(a+b\right)\)
\(=\left(a+b\right)\left(x^2-6x+9\right)\)
\(=\left(a+b\right)\left(x-3\right)^2\)
bn làm sai rồi kìa bn
-6x nhân với b là ra âm 6bx rùi bn
mà đề cho là dương 6bx
Bài làm :
+) \(-4a-8b-12c\)
\(=-4\left(a+2b+3c\right)\)
+) \(-5x-10xy-15y=-5\left(x+2xy+3y\right)\)
+) \(ax+a=a\left(x+1\right)\)
+) \(a-2ax-4ay=-a\left(1+2x+4y\right)\)
1. = 2(a+b)
2. =2(a-b)
3.=2(a+2b-3c)
4.=3(a-2b-3c)
5.=-4(a+2b+3c)
6.=-5(x+2xy+3y)
7.=-7(a+2ab+3b)
8.=6(xy-2x-3y)
9.=8(xy-3y+2x)
10.=9(ab-2a+1)
Lần sau bn cần ghi đề rõ ràng hơn
11.=x(y-1)
12.=a(x+1)
13.=m(x+y+1)
14.=-a(x+y+1)
15.=-a(x2+x+1)
16.=-2a(x+2y)
17.=2a(x-y+1)
18.=2(2ax-ay-2)
19.=5a(1-2x-3)
20.=-2ab(a+2b+3)
1)
\(x^2+4xy+4y^2-a^2+2ab-b^2\)
\(=(x^2+4xy+4y^2)-(a^2-2ab+b^2)\)
\(=(x+2y)^2-(a-b)^2\)
\(=(x+2y-a+b)(x+2y+a-b)\)
2)
\(m^2-6m+9-x^2+4xy-4y^2\)
\(=(m^2-6m+9)-(x^2-4xy+4y^2)\)
\(=(m-3)^2-(x-2y)^2\)
\(=[(m-3)-(x-2y)][(m-3)+(x-2y)]\)
\(=(m-3-x+2y)(m-3+x-2y)\)
3)
\(ax^2+bx^2+2axy+2bxy+ay^2+by^2\)
\(=a(x^2+y^2+2xy)+b(x^2+2xy+y^2)\)
\(=a(x+y)^2+b(x+y)^2\)
\(=(a+b)(x+y)^2\)
4)
\(ax^2+bx^2+6ax+6bx+9a+9b\)
\(=(ax^2+6ax+9a)+(bx^2+6bx+9b)\)
\(=a(x^2+6x+9)+b(x^2+6b+9)\)
\(=a(x+3)^2+b(x+3)^2=(a+b)(x+3)^2\)
5)
\(8a^2xy-18b^2xy\)
\(=2xy(a^2-9b^2)=2xy[a^2-(3b)^2]\)
\(=2xy(a-3b)(a+3b)\)
1) \(x^2+4xy+4y^2-a^2+2ab-b^2\)
\(=\left(x+y\right)^2-\left(a-b\right)^2\)
\(=\left(x+y-a+b\right)\left(x+y+a-b\right)\)
4) \(ax^2+bx^2-6ax+6bx+9a+9b\)
\(=\left(ax^2-6ax+9a\right)+\left(bx^2+6bx+9b\right)\)
\(=a\left(x^2-6x+9\right)+b\left(x^2+6x+9\right)\)
\(=a\left(x-3\right)^2+b\left(x+3\right)^2\)
\(ay^2-4ay+4a-by^2+4by-4b\)
\(=\left(ay^2-4ay+4a\right)-\left(by^2-4by+4b\right)\)
\(=a\left(y^2-4y+4\right)-b\left(y^2-4y+4\right)\)
\(=a\left(y-2\right)^2-b\left(y-2\right)^2\)
\(=\left(y-2\right)^2\left(a-b\right)\)
\(=\left(4ay+ax\right)-\left(6bx+24by\right)\\ =a\left(4y+x\right)-6b\left(4y+x\right)=\left(a-6b\right)\left(x+4y\right)\)
cảm ơn bạn nha