## Toán Lớp 8: Tính: a.(x+3y)(x ² – 2xy+y) b.(6x+1) ²+(6x-1) ²-2(36x ²-1) c.(2x^5-5x ³+x ²+3x-1):(x ²-1) d.(x ²-81+y ²-2xy):(x-y-9)

Question

Toán Lớp 8: Tính:
a.(x+3y)(x ² – 2xy+y)
b.(6x+1) ²+(6x-1) ²-2(36x ²-1)
c.(2x^5-5x ³+x ²+3x-1):(x ²-1)
d.(x ²-81+y ²-2xy):(x-y-9), hướng dẫn giải giúp em bài này ạ, em cảm ơn thầy cô và các bạn nhiều.

in progress 0
3 ngày 2022-12-22T16:57:42+00:00 2 Answers 0 views 0

## TRẢ LỜI ( 2 )

1. a)
(x+3y)(x^2 – 2xy + y)
=  x . x^2 – x . 2xy + x . y + 3y . x^2 – 3y . 2xy + 3y . y
= x^3 – 2x^2y + xy + 3x^2y – 6xy^2 + 3y^2
= x^3 + (3x^2y – 2x^2y) + xy – 6xy^2 + 3y^2
= x^3 + x^2y + xy – 6xy^2 + 3y^2
b)
(6x+1)^2 + (6x-1)^2 – 2 (36x^2 – 1)
= (6x+1)^2 + (6x-1)^2 – 2 (6x-1)(6x+1)
= [ (6x+1) – (6x-1)]^2
=  (6x + 1 – 6x + 1)^2
= 2^2
= 4
c)
(2x^5 – 5x^3 + x^2 + 3x – 1) : (x^2 – 1)
= [ (2x^5 – 2x^3) – (3x^3 -3x) + (x^2 – 1)] : (x^2 – 1)
= [ 2x^3 (x^2-1) – 3x (x^2 – 1) + (x^2 -1)] : (x^2-1)
= (2x^3  -3x +1)(x^2 – 1) : (x^2-1)
=  2x^3 – 3x + 1
d)
(x^2 – 81 + y^2 – 2xy) : (x-y-9)
= [ (x^2 – 2xy + y^2) – 81] : (x-y-9)
=  [(x-y)^2 – 9^2 ] : (x-y-9)
= (x-y+9)(x-y-9) : (x-y-9)
= x-y+9

2. Hướng dẫn trả lời:
a) (x + 3y)(x^2 – 2xy + y)
= xcdot(x^2 – 2xy + y) + 3ycdot(x^2 – 2xy + y)
= xcdotx^2 + xcdot(- 2xy) + xcdoty + 3ycdotx^2 + 3ycdot(- 2xy) + 3ycdoty
= x^3 – 2x^2y + xy + 3x^2y – 6xy^2 + 3y^2
= x^3 + (- 2x^2y + 3x^2y) – 6xy^2 + 3y^2 + xy
= x^3 + x^2y – 6xy^2 + 3y^2 + xy
b) (6x + 1)^2 + (6x – 1)^2 – 2cdot(36x^2 – 1)
= (6x + 1)^2 – 2cdot[(6x)^2 – 1^2] + (6x – 1)^2
= (6x + 1)^2 – 2cdot(6x + 1)cdot(6x – 1) + (6x – 1)^2
= [(6x + 1) – (6x – 1)]^2
= (6x + 1 – 6x + 1)^2
= [(6x – 6x) + (1 + 1)]^2
= 2^2
= 4
c) (2x^5 – 5x^3 + x^2 + 3x – 1) ÷ (x^2 – 1)
= (2x^5 – 2x^3 – 3x^3 + 3x + x^2 – 1) ÷ (x^2 – 1)
= [(2x^5 – 2x^3) – (3x^3 – 3x) + (x^2 – 1)] ÷ (x^2 – 1)
= [2x^3cdot(x^2 – 1) – 3xcdot(x^2 – 1) + (x^2 – 1)] ÷ (x^2 – 1)
= (2x^3 – 3x + 1)cdot(x^2 – 1) ÷ (x^2 – 1)
= 2x^3 – 3x + 1
d) (x^2 – 81 + y^2 – 2xy) ÷ (x – y – 9)
= [(x^2 – 2xy + y^2) – 81] ÷ (x – y – 9)
= [(x – y)^2 – 9^2] ÷ (x – y – 9)
= [(x – y) + 9]cdot[(x – y) – 9] ÷ (x – y – 9)
= (x – y + 9)cdot(x – y – 9) ÷ (x – y – 9)
= (x – y + 9)