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a) \(4x^2-4xy+y^2-9\)
\(=\left(2x-y\right)^2-3^2\)
\(=\left(2x-y+3\right)\left(2x-y-3\right)\)
b) \(x^2-36+4xy+4y^2\)
\(=\left(4y^2+4xy+x^2\right)-36\)
\(=\left(2y+x\right)^2-6^2\)
\(=\left(2y+x+6\right)\left(2y+x-6\right)\)
c) \(9x^2-12xy-25+4y^2\)
\(=\left(9x^2-12xy+4y^2\right)-25\)
\(=\left(3x-2y\right)^2-5^2\)
\(=\left(3x-2y+5\right)\left(3x-2y-5\right)\)
d) \(25x^2+10x-4y^2+1\)
\(=\left(25x^2+10x+1\right)-4y^2\)
\(=\left(5x+1\right)^2-\left(2y\right)^2\)
\(=\left(5x+2y+1\right)\left(5x-2y+1\right)\)
a) x^2 + 2x + 1
=\(x^2+2.x.1+1^2\)
\(=\left(x+1\right)^2\)
b) x^2 + 6x + 9
=\(x^2+2.x.3+3^2\)
\(=\left(x+3\right)^2\)
c) x^2 - 6x + 9
\(=x^2-2.x.3+3^2\)
=\(\left(x-3\right)^2\)
d) x^2 - 2x + 1
\(=x^2-2.x.1+1^2\)
\(=\left(x-1\right)^2\)
e ) 4x^2 + 4xy +y^2
\(=\left(2x\right)^2+2.2x.y+y^2\)
\(=\left(2x+y\right)^2\)
f) x^2 + 4xy + 4y^2
\(=x^2+2.x.2y+\left(2y\right)^2\)
\(=\left(x+2y\right)^2\)
phân tích các đa thức sau thành nhân tử
a) x^2 + 2x + 1
\(=\left(x+1\right)^2\)
b) x^2 + 6x + 9
\(=\left(x+3\right)^2\)
c) x^2 - 6x + 9
\(=\left(x-3\right)^2\)
d) x^2 - 2x + 1
\(=\left(x-1\right)^2\)
e ) 4x^2 + 4xy +y^2
\(=\left(2x\right)^2+4xy+y^2\)
\(=\left(2x+y\right)^2\)
f) x^2 + 4xy + 4y^2
\(=x^2+4xy+\left(2y\right)^2\)
\(=\left(x+2y\right)^2\)
p/s: --.--
a) \(\left(x^2-2x+1\right)-\left(y^2+2y+1\right)\)
\(=\left(x-1\right)^2-\left(y+1\right)^2\)
\(=\left(x-y-2\right)\left(x+y\right)\)
a) \(x^3-4x=0\)
\(x\left(x^2-4\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x^2-4=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x=\pm2\end{cases}}}\)
b) \(5x\left(3x-2\right)=4-9x^2\)
\(5x\left(3x-2\right)-\left(4-9x^2\right)=0\)
\(5x\left(3x-2\right)-\left(2-3x\right)\left(2+3x\right)=0\)
\(5x\left(3x-2\right)+\left(3x-2\right)\left(2+3x\right)=0\)
\(\left(3x-2\right)\left(5x+3x+2\right)=0\)
\(\left(3x-2\right)\left(8x+2\right)=0\)
\(\Rightarrow\orbr{\begin{cases}3x-2=0\\8x+2=0\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{2}{3}\\x=\frac{-1}{4}\end{cases}}}\)
c) \(x^2+7x=8\)
\(x^2+7x-8=0\)
\(x^2+8x-x-8=0\)
\(x\left(x+8\right)-\left(x+8\right)=0\)
\(\left(x+8\right)\left(x-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x+8=0\\x-1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-8\\x=1\end{cases}}}\)
d) \(2x^2+4y^2+10x+4xy=-25\)
\(x^2+x^2+4y^2+10x+4xy+25=0\)
\(\left(4y^2+4xy+x^2\right)+\left(x^2+10x+25\right)=0\)
\(\left(2y+x\right)^2+\left(x+5\right)^2=0\)
\(\Rightarrow\hept{\begin{cases}2y+x=0\\x+5=0\end{cases}\Rightarrow\hept{\begin{cases}y=\frac{5}{2}\\x=-5\end{cases}}}\)
1:
a) \(x^3+2x^2+x=x\left(x^2+2x+1\right)=x\left(x+1\right)^2\)
b) \(25-x^2+4xy-4y^2=25-\left(x-2y\right)^2=\left(5-x+2y\right)\left(5+x-2y\right)\)
2
\(-2x^2-4x+6=0\)
\(\Leftrightarrow-2\left(x^2+2x-3\right)=0\)
\(\Leftrightarrow x^2-x+3x-3=0\)
\(\Leftrightarrow x\left(x-1\right)+3\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x-1=0\\x+3=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=1\\x=-3\end{array}\right.\)
1,
a) x( x2 + 2x +1) = x(x+1)2
b)25 - (x-2y)2 = (5-x+2y)(5+x-2y)
2,
(x-1)(x+3)=0
<=>x=1 hoặc x=-3
a) \(4x^2-12x+9\)
\(=\left(2x\right)^2-2.2x.3+3^2\)
\(=\left(2x-3\right)^2\)
b) \(4x^2+4x+1\)
\(=\left(2x\right)^2+2.2x.1+1^2\)
\(=\left(2x+1\right)^2\)
c) \(1+12x+36x^2\)
\(=1^2+2.1.6x+\left(6x\right)^2\)
\(=\left(1+6x\right)^2\)
d) \(9x^2-24xy+16y^2\)
\(=\left(3x\right)^2-2.3x.4y+\left(4y\right)^2\)
\(=\left(3x-4y\right)^2\)
e) \(\frac{x^2}{4}+2xy+4y^2\)
\(=\left(\frac{x}{2}\right)^2+2.\frac{x}{2}.2y+\left(2y\right)^2\)
\(=\left(\frac{x}{2}+2y\right)^2\)
f) \(-x^2+10x-25\)
\(=-\left(x^2-10x+25\right)\)
\(=-\left(x^2-2.5x+5^2\right)\)
\(=-\left(x-5\right)^2\)
g) \(-16a^4b^6-24a^5b^5-9a^6b^4\)
\(=-a^4b^4\left(16b^2+24ab+9a^2\right)\)
\(=-a^4b^4\left[\left(4b\right)^2+2.4b.3a+\left(3a\right)^2\right]\)
\(=-a^4b^4\left(4b+3a\right)^2\)
h) \(25x^2-20xy+4y^2\)
\(=\left(5x\right)^2-2.5x.2y+\left(2y\right)^2\)
\(=\left(5x-2y\right)^2\)
i) \(25x^4-10x^2y+y^2\)
\(=\left(5x^2\right)^2-2.5x^2y+y^2\)
\(=\left(5x^2-y\right)^2\)
a) \(4x^2-12x+9\)
\(=\left(2x\right)^2-2.2.3+3^2\)
\(=\left(2x-3\right)^2\)
b) \(4x^2+4x+1\)
\(=\left(2x\right)^2+2.2x.1+1^2\)
\(=\left(2x+1\right)^2\)
c) \(1+12x+36x^2\)
\(=1^2+2.6x+\left(6x\right)^2\)
\(=\left(1+6x\right)^2\)
d) \(9x^2-24xy+16y^2\)
\(=\left(3x\right)^2-2.3x.4y+\left(4y\right)^2\)
\(=\left(3x-4y\right)^2\)
e) Viết = công thức trực quan hộ mình
f) \(-x^2+10x-25\)
\(=-\left(x^2-10x+25\right)\)
\(=-\left(x^2-2.5x+5^2\right)\)
\(=-\left(x-5\right)^2\)
phân tích các đa thức sau thành nhân tử
a) 4x^2 - 4xy + 4y^2
\(=\) \(\left(2x\right)^2-4xy+\left(2y\right)^2\)
\(=\left(2x-2y\right)^2\)
b) x^2 - 4xy +4y^2
\(=x^2-4xy+\left(2y\right)^2\)
\(=\left(x-2y\right)^2\)
c) x^2 + 10x + 25
\(=x^2+2.x.5+5^2\)
\(=\left(x+5\right)^2\)
d)x^2 - 10x + 25
\(=x^2-2.x.5+5^2\)
\(=\left(x-5\right)^2\)
e) 81 - (x+1)^2
\(=9^2-\left(x+1\right)^2\)
\(=\left(9-x-1\right)\left(9+x+1\right)\)
f) 16x^2 - 64 (y + 1)^2
\(=16x^2-8^2\left(y+1\right)^2\)
\(=16x^2-\left(8y+8\right)^2\)
\(=\left(16-8y-8\right)\left(16+8y+8\right)\)
p/s: ko chắc câu cuối đâu :v
ý a sai r` kìa, ý f thì x đâu mất r`?_?