rút gọn biểu thức
a/ (x+8) ² – 2(x + 8)(x – 2) + (2 – x) ²
b/ x ² (x – 4)(x + 4) – ( x ² + 1)(x ² – 1)
c/ (x + 1)(x ² – x + 1) – (x – 1)(x ² + x + 1)
d/ 5(2x – 1) ² + 4(x – 1)(x + 3) – 2(2x – 1)(3x + 1)
rút gọn biểu thức
a/ (x+8) ² – 2(x + 8)(x – 2) + (2 – x) ²
b/ x ² (x – 4)(x + 4) – ( x ² + 1)(x ² – 1)
c/ (x + 1)(x ² – x + 1) – (x – 1)(x ² + x + 1)
d/ 5(2x – 1) ² + 4(x – 1)(x + 3) – 2(2x – 1)(3x + 1)
Đáp án:
a, 100
b, – 16x² + 1
c, 2
d, 12x² – 10x – 5
Giải thích các bước giải:
a, (x + 8)² – 2(x + 8)(x – 2) + (2 – x)²
= (x + 8)² – 2(x + 8)(x – 2) + (x – 2)²
= [x + 8 – (x – 2)]² = (x + 8 – x + 2)²
= 10² = 100
b, x²(x – 4)(x + 4) – (x² + 1)(x² – 1)
= x²(x² – 16) – (x⁴ – 1)
= x⁴ – 16x² – x⁴ + 1
= – 16x² + 1
c, (x +1)(x² – x +1) – (x -1)(x² +x +1)
= x³ + 1 – (x³ – 1)
= x³ + 1 – x³ + 1 = 2
d, 5(2x – 1)² + 4(x – 1)(x + 3) – 2(2x – 1)(3x + 1)
= 5(4x² – 4x + 1) + 4(x² + 2x – 3) – 2(6x² – x – 1)
= 20x² – 20x + 5 + 4x² + 8x – 12 – 12x² + 2x + 2
= 12x² – 10x – 5
Đáp án:
Giải thích các bước giải:
a/ $(x+8)^2-2(x+8)(x-2)+(2-x)^2$
$=(x+8)^2-2(x+8)(x-2)+(x-2)^2$
$=[(x+8)-(x-2)]^2$
$=10^2=100$
b/ $x^2(x-4)(x+4)-(x^2+1)(x^2-1)$
$=x^2(x^2-16)-(x^4-1)$
$=x^4-16x^2-x^4+1$
$=-16x^2+1$
c/ $(x+1)(x^2-x+1)-(x-1)(x^2+x+1)$
$=x^3+1-(x^3-1)$
$=x^3+1-x^3+1$
$=2$
d/ $5(2x-1)^2+4(x-1)(x+3)-2(2x-1)(3x+1)$
$=5(4x^2-4x+1)+4(x^2-x+3x-3)-2(6x^2-3x+2x-1)$
$=20x^2-20x+5+4x^2-4x+12x-12-12x^2+6x-4x+2$
$=12x^2-16x-5$
chúc bạn học tốt !!!