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22 tháng 7 2017
1. \(125x^3+y^6=\left(5x\right)^3+\left(y^2\right)^3\)
\(=\left(5x+y^2\right)\left[\left(5x\right)^2-5x.y^2+\left(y^2\right)^2\right]\)
\(=\left(5x+y^2\right)\left(25x^2-5xy^2+y^4\right)\)
2. \(4x\left(x-2y\right)+8y\left(2y-x\right)\)
\(=4x\left(x-2y\right)-8y\left(x-2y\right)\)
\(=\left(x-2y\right)\left(4x-8y\right)\)
3. \(25\left(x-y\right)^2-16\left(x+y\right)^2\)
\(=\left[5\left(x-y\right)\right]^2-\left[4\left(x+y\right)\right]^2\)
\(=\left[5\left(x-y\right)-4\left(x+y\right)\right]\left[5\left(x-y\right)+4\left(x+y\right)\right]\)
\(=\left(5x-5y-4x-4y\right)\left(5x-5y+4x+4y\right)\)
\(=\left(x-9y\right)\left(9x-y\right)\)
4. \(x^4-x^3-x^2+1\)
\(=x^3\left(x-1\right)-\left(x^2-1\right)\)
\(=x^3\left(x-1\right)-\left(x-1\right)\left(x+1\right)\)
\(=\left(x-1\right)\left(x^3-x-1\right)\)
5. \(a^3x-ab+b-x\)
\(=a^3x-x-ab+b\)
\(=x\left(a^3-1\right)-b\left(a-1\right)\)
\(=x\left(a-1\right)\left(a^2+a+1\right)-b\left(a-1\right)\)
\(=\left(a-1\right)\left[x\left(a^2+a+1\right)-b\right]\)
6. \(x^3-64=x^3-4^3\)
\(=\left(x-4\right)\left(x^2+4x+16\right)\)
7. \(0,125\left(a+1\right)^3-1\)
\(=\left[0,5\left(a+1\right)\right]^3-1^3\)
\(=\left[0,5\left(a+1\right)-1\right]\left\{\left[0,5\left(a+1\right)\right]^2+\left[0,5\left(a+1\right).1\right]+1^2\right\}\)
\(=\left[0,5\left(a+1-2\right)\right]\left[0,25a^2+0,5a+0,25+0,5a+0,5+1\right]\)
\(=\left[0,5\left(a-1\right)\right]\left(0,25a^2+a+1,75\right)\)
8. \(9\left(x+5\right)^2-\left(x-7\right)^2\)
\(=\left[3\left(x+5\right)\right]^2-\left(x-7\right)^2\)
\(=\left(3x+15-x+7\right)\left(3x+15+x-7\right)\)
\(=\left(2x+22\right)\left(4x+8\right)\)
9. \(49\left(y-4\right)^2-9\left(y+2\right)^2\)
\(=\left[7\left(y-4\right)\right]^2-\left[3\left(y+2\right)\right]^2\)
\(=\left(7y-28-3y-6\right)\left(7y-28+3y+6\right)\)
\(=\left(4y-34\right)\left(10y-22\right)\)
10. \(x^2y+xy^2-x-y=xy\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(xy-1\right)\)
11. \(x^3+3x^2+3x+1-27z^3\)
\(=\left(x+1\right)^3-\left(3z\right)^3\)
\(=\left(x+1-3z\right)\left(x^2+2x+1+3xz+3z+9z^2\right)\)
12. \(x^2-y^2-x+y=\left(x-y\right)\left(x+y\right)-\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-1\right)\)
3 tháng 7 2016
a) \(x^3+3.2x^2y+3.2^2.x.y^2+\left(2y\right)^3=\left(x+2y\right)^3\)
b) áp dụng HDT : \(a^2-b^2=\left(a-b\right)\left(a+b\right)\)
\(\Rightarrow\left(2x+1-x+1\right)\left(2x+1+x-1\right)=3x\left(x+2\right)\)
c) cũng áp dụng hdt :\(a^2-b^2=\left(a-b\right)\left(a+b\right)\)
\(\Leftrightarrow\left[3\left(x+5\right)\right]^2-\left(x-7\right)^2=\left[3\left(x+5\right)-x+7\right]\left[3\left(x+5\right)+x-7\right]\)\(=\left(3x+15-x+7\right)\left(2x+15+x-7\right)=\left(2x+22\right)\left(3x+8\right)=2\left(x+11\right)\left(3x+8\right)\)
d) áp dụng típ \(a^2-b^2=\left(a-b\right)\left(a+b\right)\)
\(\Leftrightarrow\left[5\left(x-y\right)\right]^2-\left[4\left(x+y\right)\right]^2=\left[5\left(x-y\right)-4\left(x+y\right)\right]\left[5\left(x-y\right)+4\left(x+y\right)\right]\)
\(=\left(5x-5y-4x-4y\right)\left(5x-5y+4x+4y\right)=\left(x-9y\right)\left(9x-y\right)\)
e)Áp dụng típ Hdt như trên
\(\left[7\left(y-4\right)\right]^2-\left[3\left(y+2\right)\right]^2=\left[7\left(y-4\right)-3\left(y+2\right)\right]\left[7\left(y-4\right)+3\left(y+2\right)\right]\)
\(=\left(7y-28-3y-6\right)\left(7y-28+3y+6\right)=\left(4y-34\right)\left(11y-22\right)\)
\(=2\left(2y-17\right).11\left(y-2\right)=22\left(2y-17\right)\left(y-2\right)\)
Bạn 1 cái t i c k nha thật sự rất cảm ơn
3 tháng 8 2019
dấu <=> thứ 4 em làm nhầm rồi, 4x - 6x = - 2x chứ! Rồi tiếp theo em nên đưa về hằng đẳng thức chứ giải vậy ko đc đâu.
12 tháng 8 2022
a: =>\(x^3+8-x^3-2x=15\)
=>2x=-7
hay x=-7/2
c: =>(5x-3)(5x+3)=0
=>x=3/5 hoặc x=-3/5
d: =>\(x^2+8x+16-x^2+1=16\)
=>8x+1=0
hay x=-1/8
28 tháng 7 2022
a: \(125-x^6=\left(5-x^2\right)\left(5+5x^2+x^4\right)\)
b: \(=\left(x^2+1-3\right)^2=\left(x^2-2\right)^2\)
c: \(=\left(3x+15\right)^2-\left(x+7\right)^2\)
\(=\left(3x+15+x+7\right)\left(3x+15-x-7\right)\)
\(=\left(4x+22\right)\left(2x+8\right)\)
\(=2\left(2x+1\right)\left(x+4\right)\)
d: \(=9-\left(x-y\right)^2\)
\(=\left(3-x+y\right)\left(3+x-y\right)\)
e: \(=x\left(x^2+2xy+y^2-9\right)\)
\(=x\left(x+y-3\right)\left(x+y+3\right)\)
28 tháng 9 2019
a) (3x-1)(9x2+3x+1)=27x3-1
27x3-1=27x3-1
27x3-1-(27x3-1)=0
27x3-1-27x3+1=0
⇒x=0
b)(x2-5x+25)(x+5)=x3+125
(x+5)(x2-x.5+52)=x3+125
x3+125-(x3+125)=0
x3+125-x3-125=0
⇒x=0
c)(x-3)(x2-6x+9)=(x-3)3
x3-33-(x-3)3=0
x3-27-x3+27=0
⇒x=0
VM
28 tháng 9 2019
d) Đề phải là thế này chứ \(\left(x-y+4\right).\left(x-y-4\right)\)
\(=\left(x-y\right)^2-4^2\)
\(=\left(x-y\right)^2-16\)
\(=x^2-2.x.y+y^2-16\)
\(=x^2-2xy+y^2-16.\)
Chúc bạn học tốt!
a.\(9.\left(x+5\right)^2-\left(x-7\right)^2\)
\(=3^2.\left(x+5\right)^2-\left(x-7\right)^2\)
\(=\left(x+8\right)^2-\left(x-7\right)^2\)
\(=\left(x+8-x+7\right)\left(x+8+x-7\right)\)
\(=15\left(2x+1\right)\)
\(=30x+15\)
b.\(49\left(y-4\right)^2-9\left(y-2\right)^2\)
\(=7^2.\left(y-4\right)^2-3^2\left(y-2\right)^2\)
\(=\left(y+3\right)^2-\left(y+1\right)^2\)
\(=\left(y+3-y-1\right)\left(y+3+y+1\right)\)
\(=2\left(2y+4\right)\)
\(=4y+8\)
a./ \(=\left[3\left(x+5\right)\right]^2-\left(x-7\right)^2=\left(3x+15-x+7\right)\left(3x+15+x-7\right)=\left(2x+22\right)\left(4x+8\right).\)
\(=8\left(x+11\right)\left(x+2\right).\)
b./ \(=\left[7\left(y-4\right)\right]^2-\left[3\left(y-2\right)\right]^2=\left(7y-28+3y-6\right)\left(7y-28-3y+6\right)=\left(10y-34\right)\left(4y-22\right)\)
\(=4\left(5y-17\right)\left(2y-11\right)\)