Khai triển các hằng đẳng thức sau: a, (2x+1)^2 – (x-2)^2 b, 64x^2 – (x+1)^2 c, (x+3)^2 – 4x^2 23/08/2021 Bởi Aaliyah Khai triển các hằng đẳng thức sau: a, (2x+1)^2 – (x-2)^2 b, 64x^2 – (x+1)^2 c, (x+3)^2 – 4x^2
Đáp án: a, (2x+1)² – (x-2)² = (2x + 1 – x + 2)(2x + 1+ x – 2) =(x + 3)(3x – 1) =3x² + 8x -3 b, 64x² – (x + 1)² = (8x)² – (x + 1)² = (8x – x – 1)(8x + x + 1) =(7x – 1)(9x + 1) =63x² – 2x -1 c, (x + 3)² – 4x² = x²+ 6x + 9-4x² = -3x²+6x+9 Bình luận
a, (2x+1)² – (x-2)² ⇔ (2x+1-x+2).(2x + 1+ x – 2) ⇔ (x + 3).(3x – 1) ⇔ 3x² + 8x -3 ____________________ b, 64x² – (x+1)² ⇔(8x)² – (x+1)² ⇔ (8x-x-1).(8x+x+1) ⇔ 63x² – 2x-1 ________________ c, (x+3)²- 4x² ⇔ x²+6x+ 9 -4x² ⇔ -3x²+6x+9 Bình luận
Đáp án:
a, (2x+1)² – (x-2)²
= (2x + 1 – x + 2)(2x + 1+ x – 2)
=(x + 3)(3x – 1)
=3x² + 8x -3
b, 64x² – (x + 1)²
= (8x)² – (x + 1)²
= (8x – x – 1)(8x + x + 1)
=(7x – 1)(9x + 1)
=63x² – 2x -1
c, (x + 3)² – 4x²
= x²+ 6x + 9-4x²
= -3x²+6x+9
a, (2x+1)² – (x-2)²
⇔ (2x+1-x+2).(2x + 1+ x – 2)
⇔ (x + 3).(3x – 1)
⇔ 3x² + 8x -3
____________________
b, 64x² – (x+1)²
⇔(8x)² – (x+1)² ⇔ (8x-x-1).(8x+x+1)
⇔ 63x² – 2x-1
________________
c, (x+3)²- 4x²
⇔ x²+6x+ 9 -4x²
⇔ -3x²+6x+9