Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
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) \(-x^2+10x-25\)
\(=-\left(x^2-10x+25\right)\)
\(=-\left(x^2-2.5x+5^2\right)\)
\(=-\left(x-5\right)^2\)
a) a3 - a2c + a2b - abc
= a( a2 - ac + ab - bc )
= a[ a( a - c ) + b( a - c ) ]
= a( a - c )( a + b )
b) ( x2 + 1 )2 - 4x2
= ( x2 + 1 )2 - ( 2x )2
= ( x2 - 2x + 1 )( x2 + 2x + 1 )
= ( x - 1 )2( x + 1 )2
c) x2 - 10x - 9y2 + 25
= ( x2 - 10x + 25 ) - 9y2
= ( x - 5 )2 - ( 3y )2
= ( x - 3y - 5 )( x + 3y - 5 )
d) 4x2 - 36x + 56
= 4( x2 - 9x + 14 )
= 4( x2 - 7x - 2x + 14 )
= 4[ x( x - 7 ) - 2( x - 7 ) ]
= 4( x - 7 )( x - 2 )
a,\(a^3-a^2c+a^2b-abc\)
\(=a\left(a^2-ac+ab-bc\right)\)
\(=a\left[a\left(a-c\right)+b\left(a-c\right)\right]\)
\(=a\left(a-b\right)\left(a-c\right)\)
b,\(\left(x^2+1\right)^2-4x^2\)
\(=\left(x^2+1-2x\right)\left(x^2+1+2x\right)\)
\(=\left(x-1\right)^2\left(x+1\right)^2\)
c,\(x^2-10x-9y^2+25\)
\(=\left(x^2-10x+25\right)-9y^2\)
\(=\left(x-5\right)^2-\left(3y\right)^2\)
\(=\left(x-5-3y\right)\left(x-5+3y\right)\)
d,\(4x^2-36x+56\)
\(=4\left(x^2-9x+14\right)\)
\(=4\left(x^2-7x-2x+14\right)\)
\(=4\left(x-7\right)\left(x-2\right)\)
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) \(25x^4-10x^2y+y^2\)
\(=\left(5x^2\right)^2-2.5x^2y+y^2\)
\(=\left(5x^2-y\right)^2\)
Bài 1: (2 điểm) Phân tích các đa thức sau thành nhân tử
a) a3 – a2c + a2b – abc
= a(a2 - ac + ab - bc)
= a[a(a - c) + b(a - c)]
= a(a - c)(a + b)
b) (x2 + 1)2 – 4x2
= (x2 + 1)2 – (2x)2
= (x2 + 1 - 2x)(x2 + 1 + 2x)
= (x - 1)2. (x + 1)2
c) x2 – 10x – 9y2 + 25
= (x2 - 10x + 25) - 9y2
= (x - 5)2 - (3y)2
= (x - 5 + 3y)(x - 5 - 3y)
d) 4x2 – 36x + 56
= 4x2 - 28x - 8x + 56
= (4x2 - 28x) - (8x - 56)
= 4x(x - 7) - 8(x - 7)
= (x - 7)(4x - 8)
= 4(x - 7)(x - 2)
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) \(2x^2+4y^2+10x+4xy=-25\)
\(x^2+x^2+4y^2+10x+4xy+25=0\)
\(\left(4y^2+4xy+x^2\right)+\left(x^2+10x+25\right)=0\)
\(\left(2y+x\right)^2+\left(x+5\right)^2=0\)
\(\Rightarrow\hept{\begin{cases}2y+x=0\\x+5=0\end{cases}\Rightarrow\hept{\begin{cases}y=\frac{5}{2}\\x=-5\end{cases}}}\)
a) \(2x^3-4x^2+2x\)
\(=2x\left(x^2-2x+1\right)\)
\(=2x\left(x-1\right)^2\)
b) \(x^3+2x^2+4x\)
\(=x\left(x^2+2x+4\right)\)
c) \(2x^3+8x^2+8x\)
\(=2x\left(x^2+4x+4\right)\)
\(=2x\left(x+2\right)^2\)
d) \(36x^2-a^2+10a-25\)
\(=36x^2-\left(a^2-10a+25\right)\)
\(=\left(6x\right)^2-\left(a-5\right)^2\)
\(=\left(6x-a+5\right)\left(6x+a-5\right)\)
p/s: lần sau gõ đề cẩn thận hơn nhé.
a, -x - y2 + x2 - y = (x2 - y2) - (x + y)
= (x - y)(x + y) - (x + y)
= (x + y)(x - y - 1)
b, x( x + y ) - 5x - 5y = x(x + y) - 5(x + y)
= (x - 5)(x + y)
c, x2 - 5x + 5y - y2 = (x - y)(x + y) - 5(x - y)
= (x - y)(x + y - 5)
d, 5x3 - 5x2y - 10x2 + 10xy = 5x2(x - y) - 10x(x - y)
= 5x(x - y)(x - 2)
e, 27x3 - 8y3 = (3x - 2y)(9x2 + 6xy + 4y2)
f, x2 - y2 - x - y = (x - y)(x + y) - (x + y)
= (x + y)(x - y - 1)
g, x2 - y2 - 2xy + y2 = (x2 - 2xy + y2) - y2
= (x - y)2 - y2
= (x - y - y)(x - y + y) = x(x - 2y)
h, x2 - y2 + 4 - 4x = (x2 - 4x + 4) - y2
= (x - 2)2 - y2
= (x - y - 2)(x + y - 2)
i, x3 + 3x2 + 3x + 1 - 27z3 = (x + 1)3 - 27z3
= (x+1-3z)(x2+2x+1+3xz+3z+9z2)
k, 4x2 + 4x - 9y2 + 1 = (2x + 1)2 - 9y2
= (2x - 3y + 1)(2x + 3y + 1)
m, x2 - 3x + xy - 3y = x(x - 3) + y(x - 3)
= (x - 3)(x + y)
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
<3 U love you
a) a3 - a2c + a2b - abc
= a( a2 - ac + ab - bc )
= a[ ( a2 + ab ) - ( ac + bc ) ]
= a( a( a + b ) - c( a + b ) ]
= a( a + b )( a - c )
b) ( x2 + 1 )2 - 4x2
= ( x2 + 1 )2 - ( 2x )2
= ( x2 - 2x + 1 )( x2 + 2x + 1 )
= ( x - 1 )2( x + 1 )2
c) x2 - 10x - 9y2 + 25
= ( x2 - 10x + 25 ) - 9y2
= ( x - 5 )2 - ( 3y )2
= ( x - 3y - 5 )( x + 3y - 5 )
d) 4x2 - 36x + 56
= 4x2 - 8x - 28x + 56
= 4x( x - 2 ) - 28( x - 2 )
= 4( x - 2 )( x - 7 )