– Khai triển : a, (x+5)^2
b,(y-7)^2
c, (2x+3)^2
d,(2y-1)^2
e, y^2 – 81
g, (3y+2)^3
f, 16x^2 – 225
h, (5x-3 )^3
l, (3x+2y)^3
k, (2y-1/2)^3
– Khai triển : a, (x+5)^2
b,(y-7)^2
c, (2x+3)^2
d,(2y-1)^2
e, y^2 – 81
g, (3y+2)^3
f, 16x^2 – 225
h, (5x-3 )^3
l, (3x+2y)^3
k, (2y-1/2)^3
Đáp án:
Giải thích các bước giải:
a) ( x + 5)²
= x² + 2.x.5 + 5² = x² + 10x + 25
b) ( y – 7)²
= y² – 2.y.7 + 7² = y² – 14y + 49
c) ( 2x + 3)²
= (2x)² + 2.2x.3 + 3² = 4x² +12x +9
d) ( 2y – 1)²
= ( 2y)² – 2.2y.1 + 1² = 4y² – 4y + 1
e) y² – 81 = y² – 9² = ( y – 9)( y + 9)
g) ( 3y + 2)³
= ( 3y)³ + 3.(3y)².2 + 3.3y.2² + 2³
= 27x³ + 54y² + 36y + 8
f) 16x² – 225 =( 4x)² – 15²
= ( 4x + 15)( 4x – 15)
h) ( 5x – 3)³
= ( 5x)³ – 3.(5x)².3 + 3.5x.3² – 3³
= 125x³ – 225x² + 135x – 27
l) ( 3x + 2y)³
=(3x)³ + 3.(3x)².2y + 3.3x.(2y)² + (2y)³
= 27x³ + 54x²y + 36xy² + 8y³
k) ( 2y – 1/2)³
= ( 2y)³ – 3.( 2y)².1/2 + 3.2y.(1/2)² – ( 1/2)³
= 8y³ – 6y² + 3/2y – 1/8
$a.(x+5)^2=x^2+10x+25 \\b.(y-7)^2=y^2-14y+49 \\c.(2x+3)^2=4x^2+12x+9 \\d.(2y-1)^2=4y^2-4y+1 \\e.y^2-81=(y-9)(y+9) \\g.(3y+2)^3=27y^3+54y^2+36y+8 \\f.16x^2-225=(4x-15)(4x+15) \\h.(5x-3)^3=125x^3-225x^2+135x-27 \\l.(3x+2y)^3=27x^3+54x^2y+36xy^2+8y^3 \\k.\bigg(2y-\dfrac{1}{2}\bigg)^3=8y^3-6y^2+\dfrac{3y}{2}-\dfrac{1}{8}$