phân tích đa thức thành nhân tử
1, A = 2x^2 + 5x^3 + x^2y
2, A = 4x^2y – 8xy^2 + 18x^2y^2
3, A = -3x^2y + 6x^2 y^2
4, A = 2x^3 y^4 – 4x^5 y^6 + 6y^7 x^8
5, A = 14x^2y – 21xy^2 + 28x^2 y^2
6, A = -8x^4 y^3 – 12x^2 y^4 + 20x^3 y^4
7, A = 5x . (x – 1) – 15x . (1 – x)
8, A = 2x^2 . (y – 1) – 15x . (1 – x)
9, A = 9x^2 . (y + z ) + 3x . (y + z)
10, A = 10x . ( x – y) – 8y . (y – x)
11, A = 2x . ( x + y) – 6x^2 . (x + y)
12, A = 10xy . ( x – y) – 6y . (y – x)
giải giúp e với ạ !
phân tích đa thức thành nhân tử 1, A = 2x^2 + 5x^3 + x^2y 2, A = 4x^2y – 8xy^2 + 18x^2y^2 3, A = -3x^2y + 6x^2 y^2 4, A = 2x^3 y^4 – 4x^5 y^6 + 6y^7
By Remi
1, A = 2x² + 5x³ + x²y
= x²(2 + 5x + y)
2, A = 4x²y – 8xy² + 18x²y²
= 2xy(2x – 4y + 9xy)
3, A = -3x²y + 6x²y²
= -3x²y(1 – 2y)
4, A = 2x³$y^{4}$ – 4$x^{5}$$y^{6}$ + 6$y^{7}$$x^{8}$
= 2x³$y^{4}$(1 – 2x²y² + 3$x^{5}$y³)
5, A = 14x²y – 21xy² + 28x²y²
= 7xy(2x – 3y + 4xy)
6, A = -8$x^{4}$y³ – 12x²$y^{4}$ + 20x³$y^{4}$
= -4x²y³(2x² + 3y – 5xy)
7, A = 5x . (x – 1) – 15x . (1 – x)
= 5x(x – 1) + 15(x – 1)
= (x – 1)(5x + 15)
= 5(x – 1)(x + 3)
8, A = 2x² . (y – 1) – 15x . (1 – x)
= x[2x(y – 1) – 15(1 – x)]
= x(2xy – 2 – 15 + 15x)
= x(2xy + 15x – 17)
9, A = 9x² . (y + z ) + 3x . (y + z)
= (y + z)(9x² + 3x)
= 3x(y + z)(3x + 1)
10, A = 10x . ( x – y) – 8y . (y – x)
= 10x(x – y) + 8y(x – y)
= (x – y)(10x + 8y)
= 2(x – y)(5x + 4y)
11, A = 2x . ( x + y) – 6x² . (x + y)
= (x + y)(2x – 6x²)
= 2x(x + y)(1 – 3x)
12, A = 10xy . ( x – y) – 6y . (y – x)
= 10xy(x – y) + 6y(x – y)
= (x – y)(10xy + 6y)
= 2y(x – y)(5x + 3)
(Các bước đầu tiên đều áp dụng phương pháp đặt nhân tử chung)