Toán Lớp 8: a) x^2 + xy-5x-5y b) 9x^2+6x+1-(x+1)^2 c) 5x^2-x+5xy-y d) x^3+3x^2+2x e) x^2-16+6xy+9y^2

Question

Toán Lớp 8:  a) x^2 + xy-5x-5y b) 9x^2+6x+1-(x+1)^2 c) 5x^2-x+5xy-y d) x^3+3x^2+2x e) x^2-16+6xy+9y^2

tonhu12 · Answer

Giải đáp:       Lời giải và giải thích chi tiết:   a)x^2+xy-5x-5y   =(x^2+xy)-(5x+5y)   =x(x+y)-5(x+y)   =(x+y)(x-5)       b)9x^2+6x+1-(x+1)^2   =9x^2+6x+1&minus;(x^2+2x+1)   =9x^2+6x+1&minus;x^2-2x-1   =8x^2+4x   =4x(2x+1)       c)5x^2-x+5xy-y   =(5x^2-x)+(5xy-y)   =x(5x&minus;1)+y(5x&minus;1)   =(x+y)(5x&minus;1)       d)x^3+3x^2+2x   =x(x^2+3x+2)   =x(x^2+x+2x+2)   =x[(x^2+x)+(2x+2)]   =x[x(x+1)+2(x+1)]   =x(x+1)(x+2)       e)x^2-16+6xy+9y^2   =(x+3y)^2&minus;4^2   =(x+3y&minus;4)(x+3y+4)

thanhtung · Answer

$ text{a) x&sup2; + xy - 5x - 5y }$   $ text{= x( x + y ) - 5( x + y )}$   $ text{= ( x - 5 )( x + y )}$   $ text{b) 9x&sup2; + 6x + 1 - ( x + 1 )&sup2;}$   $ text{= ( 3x + 1 )&sup2; - ( x + 1 )&sup2;}$   $ text{= ( 3x + 1 + x + 1 )( 3x + 1 - x - 1 ) }$   $ text{= ( 4x + 2 ). 2x }$   $ text{= 4x( x + 1 ) }$   $ text{c) 5x&sup2; - x + 5xy - y }$   $ text{= x( 5x - 1 ) +y( 5x - 1 )}$   $ text{= ( x + y )( 5x - 1 )}$   $ text{d) x&sup3; - 3x&sup2; + 2x }$   $ text{= x( x&sup2; - 3x + 2 ) }$   $ text{= x( x&sup2; - x - 2x + 2 )}$   $ text{= x[ x( x - 1 ) - 2( x - 1 ) ] }$   $ text{= x( x - 1 )( x - 2 )}$   $ text{e) x&sup2; - 16 + 6xy + 9y&sup2; }$   $ text{= ( x&sup2; + 6xy + 9y&sup2; ) - 16 }$   $ text{= ( x + 3y )&sup2; - 4&sup2;}$   $ text{= ( x + 3y - 4 )( x + 3y + 4 )}$