rút gọn
a/ (9x-10)² + (1 – 5x) ² + 2(9x – 1)(1 – 5x)
b/ (a + b + c) ² + ( a + b – c) ² – 2(a + b)²
c/ (2a ² + 2a + 1) ( 2a ² – 2a + 1) – (2a ² + 1) ²
d/ 6(x+1) ² – 2(x+1) ² + 2(x-1)(x ² + x +1) -1
rút gọn
a/ (9x-10)² + (1 – 5x) ² + 2(9x – 1)(1 – 5x)
b/ (a + b + c) ² + ( a + b – c) ² – 2(a + b)²
c/ (2a ² + 2a + 1) ( 2a ² – 2a + 1) – (2a ² + 1) ²
d/ 6(x+1) ² – 2(x+1) ² + 2(x-1)(x ² + x +1) -1
Đáp án:
$a/ 16x^2\\
b/2c^2\\
c/ -4a^2\\
d/ 2x^3+4x^2+8x+1\\$
Giải thích các bước giải:
$a/ (9x-1)^2 + (1 – 5x)^2 + 2(9x – 1)(1 – 5x)\\
=(9x-1+1-5x)^2\\
=(4x)^2\\
=16x^2\\
b/ (a + b + c)^2 + ( a + b – c)^2 – 2(a + b)^2\\
=(a+b)^2+2(a+b).c+c^2+(a+b)^2-2(a+b).c+c^2-2(a+b)^2\\
=2c^2\\
c/ (2a^2 + 2a + 1) ( 2a^2 – 2a + 1) – (2a^2 + 1)^2\\
=(2a^2+1)^2-(2a)^2-(2a^2+1)^2\\
=-4a^2\\
d/ 6(x+1)^2 – 2(x+1)^2 + 2(x-1)(x^2 + x +1) -1 \\
=4(x+1)^2+2(x^3-1)-1\\
=4(x^2+2x+1)+2x^3-2-1\\
=4x^2+8x+4+2x^3-3\\
=2x^3+4x^2+8x+1\\$
a/ (9x-1)² + (1 – 5x) ² + 2(9x – 1)(1 – 5x)
= (9x – 1)² + 2(9x – 1)(1 – 5x) + (1 – 5x)²
= (9x – 1 + 1 – 5x)²
= (4x)²
= 16x²
b/ (a + b + c) ² + ( a + b – c) ² – 2(a + b)²
= [(a+b)+c]² + [(a+b)-c]² – 2(a +b)²
= (a +b)² + 2(a+b)c + c² + (a+b)² – 2(a+b)c + c² – 2(a+b)²
= 2(a+b)² – 2(a+b)² + 2c²
= 2c²
c/ (2a ² + 2a + 1) ( 2a ² – 2a + 1) – (2a ² + 1) ²
= (2a² + 1 + 2a)(2a² + 1 – 2a) – (2a² + 1)²
= (2a² + 1)² – (2a)² – (2a² + 1)²
= (2a² + 1)² – (2a² + 1)² – 4a²
= -4a²
d/ 6(x+1) ² – 2(x+1) ² + 2(x-1)(x ² + x +1) -1
= 4(x + 1)² + 2(x³ – 1) – 1
= 4(x² + 2x + 1) + 2(x³ – 1) – 1
= 4x² + 8x + 4 + 2x³ – 2 – 1
= 2x³ + 4x² + 8x + 1