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\(a.a\left(b+c\right)+3b+3c=a\left(b+c\right)+3\left(b+c\right)=\left(b+c\right)\left(a+3\right)\)
\(b.a\left(c-d\right)+c-d=\left(c-d\right)\left(a+1\right)\)
\(c.b\left(a-c\right)+5a-5c=b\left(a-c\right)+5\left(a-c\right)=\left(a-c\right)\left(b+5\right)\)
\(d.a\left(m-n\right)+m-n=\left(m-n\right)\left(a+1\right)\)
\(e.mx+my+5x+5y=m\left(x+y\right)+5\left(x+y\right)=\left(x+y\right)\left(m+5\right)\)
\(f.ma+mb-a-b=m\left(a+b\right)-\left(a+b\right)=\left(a+b\right)\left(m-1\right)\)
\(g.4x+by+4y+bx=4x+bx+by+4y=x\left(b+4\right)+y\left(b+4\right)=\left(b+4\right)\left(x+y\right)\)
\(h.1-ax-x+a=\left(a+1\right)-x\left(a+1\right)=\left(a+1\right)\left(1-x\right)\)
\(k.x^{m+2}-x^m=x^m\left(x^2-1\right)=x^m\left(x-1\right)\left(x+1\right)\)
\(m.\left(a-b\right)^2-\left(b-a\right)\left(a+b\right)=\left(b-a\right)^2-\left(b-a\right)\left(a+b\right)=\left(b-a\right)\left(b-a-a-b\right)=-2a\left(b-a\right)\)
\(n.a\left(a-b\right)\left(a+b\right)-\left(a^2-2ab+b^2\right)=a\left(a-b\right)\left(a+b\right)-\left(a-b\right)^2=\left(a-b\right)\left(a^2+ab-a+b\right)\)
\(1.mx+my+5x+5y\)
\(=m\left(x+y\right)+5\left(x+y\right)\)
\(=\left(m+5\right)\left(x+y\right)\)
\(2.\left(a+b\right)\left(a-b\right)-\left(a+b\right)\left(a^2-ab+b^2\right)\)
\(=\left(a+b\right)\left(a-b-a^2+ab-b^2\right)\)
1. C. \(16x^2\left(x-y\right)\)\(-10y\left(y-1\right)\)\(=-2\left(y-x\right)\)\(\left(8x^2+5y\right)\)
2. C. \(\left(x-y\right)\left(x-y-3\right)\)
3. D. \(\left(x-2\right)\left(x+1\right)\)
4. C. \(y\left(x-2\right)\)\(5x\left(x-3\right)\)
5. D. \(3\left(x-2y\right)\)
1. Trong các kết quả sau kết quả nào sai
A. -17x^3y-34x^2y^2+51xy^3=17xy(x^2+2xy-3y^2)
B. x(y-1) +3(y-1)= -(1-y)(x+3)
C. 16x^2(x-y)-10y(y-1)=-2(y-x)(8x^2+5y)
2. Đa thức (x-y)^2+3(y-x) được phân tích thành nhân tử là:
A. (x+y)(x-y+3)
B. (x-y)(2x-2y+3)
C. (x-y)(x-y-3)
D. Cả 3 câu đều sai
3. Kết quả phân tích đa thức x(x-2)+(x-2) thành nhân tử
A. (x-2)x
B. (x-2)^2.x
C. x(2x-4)
D. (x-2)(x+1)
4. Kết quả phân tích 5x^2(xy-2y)-15x(xy-2y) thành nhân tử
A. (xy-2y)(5x^2-15x^2)
B. y(x-2)(5x^2-15x^2)
C. y(x-2)5x(x-3)
D. (xy-2y)5x(x-3)
5. Kết quả phân tích đa thức 3x-6y thành nhân tử là
A. 3(x-6y)
B. 3(3x-y)
C. 3(3x-2y)
D. 3(x-2y)
Ta có:
a) 5x - 20y = 5(x - 4y)
b) 5x(x - 1) - 3x(x - 1) = x(x - 1)2
c) x(x + y) - 5x - 5y = x(x + y) - (5x + 5y) = x(x + y) - 5(x + y) = (x - 5)(x + y)
d) x2 - 9 = (x - 3)(x + 3)
e) 42 - 25 = (4 - 5)(4 + 5) f) x6 - y6 = (x4)2 - (y4)2 = (x4 - y4)(x4 + y4)
a) 5x - 20y = 5( x - 4y)
b) 5x(x-1) - 3x(x-1) =2x (x-1)
c) x2 - 9 = x2 - 32 = ( x-3)(x+3)
e) 42-25 = 42 - 52 = ( 4-5)(4+5)= -9
f) x6 - y6 = (x3)2 - (y3)2 = ( x3 - y3 ) ( x3 + y3)
= (x-y) ( x2 + xy + y2 ) ( x+y) ( x2 -xy +y2)
a) Ta có: \(a\left(m-n\right)+m-n\)
\(=a\left(m-n\right)+\left(m-n\right)\)
\(=\left(m-n\right)\left(a+1\right)\)
b) Ta có: \(mx+my+5x+5y\)
\(=m\left(x+y\right)+5\left(x+y\right)\)
\(=\left(x+y\right)\left(m+5\right)\)
c) Ta có: \(ma+mb-a-b\)
\(=m\left(a+b\right)-\left(a+b\right)\)
\(=\left(a+b\right)\left(m-1\right)\)
d) Ta có: \(1-xa-x+a\)
\(=\left(a+1\right)-x\left(a+1\right)\)
\(=\left(a+1\right)\left(1-x\right)\)
e) Ta có: \(\left(a-b\right)^2-\left(b-a\right)\left(a+b\right)\)
\(=\left(a-b\right)^2+\left(a-b\right)\left(a+b\right)\)
\(=\left(a-b\right)\left(a-b+a+b\right)\)
\(=2a\left(a-b\right)\)
f) Ta có: \(a\left(a-b\right)\left(a+b\right)-\left(a+b\right)\left(a^2-ab+b^2\right)\)
\(=\left(a+b\right)\left(a^2-ab\right)-\left(a+b\right)\left(a^2-ab+b^2\right)\)
\(=\left(a+b\right)\left(a^2-ab-a^2+ab-b^2\right)\)
\(=b^2\cdot\left(a+b\right)\)
g) Ta có: \(3x\left(x+7\right)^2-11x^2\left(x+7\right)+9\left(x+7\right)\)
\(=\left(x+7\right)\left[3x\left(x+7\right)-11x^2+9\right]\)
\(=\left(x+7\right)\left(3x^2+21x-11x^2+9\right)\)
\(=\left(x+7\right)\left(-8x^2+21x+9\right)\)
\(=\left(x+7\right)\left(-8x^2+24x-3x+9\right)\)
\(=\left(x+7\right)\left[-8x\left(x-3\right)-3\left(x-3\right)\right]\)
\(=\left(x+7\right)\left(x-3\right)\left(-8x-3\right)\)
h) Ta có: \(\left(x+5\right)^2-3\left(x+5\right)\)
\(=\left(x+5\right)\left(x+5-3\right)\)
\(=\left(x+5\right)\left(x+2\right)\)
i) Ta có: \(2x\left(x-3\right)-3\left(x-3\right)^2\)
\(=\left(x-3\right)\left[2x-3\left(x-3\right)\right]\)
\(=\left(x-3\right)\left(2x-3x+9\right)\)
\(=\left(x-3\right)\left(9-x\right)\)
j) Ta có: \(x\left(x-7\right)+\left(7-x\right)^2\)
\(=x\left(x-7\right)+\left(x-7\right)^2\)
\(=\left(x-7\right)\left(x+x-7\right)\)
\(=\left(x-7\right)\left(2x-7\right)\)
k) Ta có: \(3x\left(x-9\right)^2-\left(9-x\right)^3\)
\(=3x\left(x-9\right)^2+\left(x-9\right)^3\)
\(=\left(x-9\right)^2\cdot\left(3x+x-9\right)\)
\(=\left(x-9\right)^2\cdot\left(4x-9\right)\)
a)5x-20y
=5x-4*5y
=5(x-4y)
b)x(x-1)-3x(x-1)
=(x-3x)(x-1)
c)x(x+y)-5x-5y
=x(x+y)-5(x+y)
=(x-5)(x+y)
a) mx + my + 5x + 5y
= m(x+y) +5(x+y)
= (m+5)(x+y)
b) ma + mb - a - b
= m(a+b) - (a+b)
= (m-1)(a+b)
c) 1 - xa - x + a
= - (xa +x) + (1+a)
= - x(a+1) + (1+a)
= (-x+1)(1+a) = (1-x)(1+a)
c) (a-b)^2 - (b-a)(a+b)
= (b-a)^2 - (b-a)(a+b) = (b-a)(b-a) - (b-a)(a+b)
= (b-a)(b-a-(a+b))
= (b-a)(b-a-a-b)
= (b-a).(-2a) = -2a(b-a) = 2a(a-b)
a) mx+my+5x+5y
= m(x+y)+5(x+y)
=(x+y)(m+5)
b) ma+mb-a-b
=m(a+b)-(a+b)
= (a+b)(m-1)
c) 1-xa-x+a
= (1-x)-(xa-a)
= (1-x)-a(x-1)
=(1-x)+a(1-x)
= (1-x)(1+a)
d) (a-b)2-(b-a)(a+b)
= (a-b)2+(a-b)(a+b)
= (a-b)[(a-b)(a+b)]
= (a-b)(a2-b2)
=(a-b)(a-b)(a+b) = (a-b)2(a+b)