Hướng dẫn giải bài tập SGK Toán lớp 8 tập 1 bài 8: Phân tích đa thức thành nhân tử bằng phương pháp nhóm hạng tử

Thứ bảy - 07/07/2018 03:54
Hướng dẫn giải bài tập SGK Toán lớp 8 tập 1 bài 8: Phân tích đa thức thành nhân tử bằng phương pháp nhóm hạng tử

Bài 47 (SGK trang 22 toán lớp 8 tập 1)

Phân tích cá đa thức sau thành nhân tử:

a) x2 – xy + x – y;                                                   b) xz + yz – 5(x + y);

c) 3x2 – 3xy – 5x + 5y.

Giải:

a) x2 – xy + x – y = (x2 – xy) + (x – y)

= x(x – y) + (x -y)

= (x – y)(x + 1)

b) xz + yz – 5(x + y) = z(x + y) – 5(x + y)

= (x + y)(z – 5)

c) 3x2 – 3xy – 5x + 5y = (3x2 – 3xy) – (5x – 5y)

= 3x(x – y) -5(x – y) = (x – y)(3x – 5).

Bài 48 (SGK trang 22 toán lớp 8 tập 1)

Phân tích các đa thức sau thành nhân tử:

a) x2 + 4x – y2 + 4;                                     b) 3x2 + 6xy + 3y2 – 3z2;

c) x– 2xy + y2 – z2 + 2zt – t2.

Giải:

a) x2 + 4x – y2 + 4 = (x2 + 4x + 4) – y2

= (x + 2)2 – y2 = (x + 2 – y)(x + 2 + y)

b) 3x2 + 6xy + 3y2 – 3z2 = 3[(x2 + 2xy + y2) – z2]

= 3[(x + y)2 – z2] = 3(x + y – z)(x + y + z)

c) x2 – 2xy + y2 – z2 + 2zt – t2 = (x2 – 2xy + y2) – (z2 – 2zt + t2)

= (x – y)2 – (z – t)2

= [(x – y) – (z – t)] . [(x – y) + (z – t)]

= (x – y – z + t)(x – y + z – t)

Bài 49 (SGK trang 22 toán lớp 8 tập 1)

Tính nhanh:

a) 37,5 . 6,5 – 7,5 . 3,4 – 6,6 . 7,5 + 3,5 . 37,5

b) 452 + 402 – 152 + 80 . 45.

Giải:

a) 37,5 . 6,5 – 7,5 . 3,4 – 6,6 . 7,5 + 3,5 . 37,5

= (37,5 . 6,5 + 3,5 . 37,5) – (7,5 . 3,4 + 6,6 . 7,5)

= 37,5(6,5 + 3,5) – 7,5(3,4 + 6,6)

= 37,5 . 10 – 7,5 . 10

= 375 – 75 = 300.

b) 452 + 402 – 152 + 80 . 45 = 45+2 . 40 . 45 + 402 – 152

= (40 + 45)2 – 152 = 852 – 152 = (85 – 15)(85 + 15) = 70 . 100 = 7000.

Bài 50 (SGK trang 23 toán lớp 8 tập 1)

Tìm x, biết:

a) x(x – 2) + x – 2 = 0;                                        b) 5x(x – 3) – x + 3 = 0

Giải:

a) x(x – 2) + x – 2 = 0

(x – 2)(x + 1) = 0

Hoặc x – 2 = 0 => x = 2

Hoặc x + 1 = 0 => x = -1

Vậy x = -1; x = 2

b) 5x(x – 3) – x + 3 = 0

5x(x – 3) – (x – 3) = 0

(x – 3)(5x – 1) = 0

Hoặc x – 3 = 0 => x = 3

Hoặc 5x – 1 = 0 => x = 1/5.

Vậy x = 1/5; x = 3

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