Question

10 example of (x+y)³ identity​

Answer 1

Answer:

(x + y)3 = x3 + 3x2y + 3xy2 + y3

(x - y)3 = x3 - 3x2y + 3xy2 - y3

Example: (1 + a2)3 = 13 + 3.12.a2 + 3.1.(a2)2 + (a2)3 = 1 + 3a2 + 3a4 + a6

Answer 2

Formula :

(x + y) ³ = x³ + 2x²y + 2xy² + y³

Examples :

1] ( x + 3 )³

= (x )³ + 2 (x)²(3) + 2(x)(3)² +(3)³

= x³ + 6x² + 18x + 27

2] ( 2 + y)³

= (2)³ + 2 (2)² y +2(2)y² + y³

= 8 + 8y + 4y² + y³

3] ( a + b) ³

= a³ + 3a²b + 3ab² + b³

= a³ + 3ab ( a + b) + b³

4] (2x + 3x )³

= (2x)³+3(2x)²(3x) +3(2x)(3x)²+ (3x)³

=8x³ + 36x³ + 54x³ + 27x³

=98x³ + 27x³

=125x³

5] (√2 + x) ³

=(√2)³ + 3(√2)²x + 3(√2)x²+(x)³

=2√2 + 6x + 3√2x² +x³

6] (z + 1)³

= (z) ³ + 2 (z)² (1) + 2(z)(1)² + (1)³

= z³ + 2z² + 2z + 1

7] (√2x + y) ³

=(√2x)³ + 2(√2x)²y + 2(√2x) y²+ y³

=2√2x³ + 4x²y + 2√2xy² + y³

8] ((3/2) + y) ³

= (3/2)³ + 2(3/2)²y + 2(3/2)y² + y³

=(27/8) + 2(9/4)y + 3y² + y³

= (27/8) +(9/2)y + 3y² + y³

9] ( x + 0 )³

= (x)³ + 2(x)²(0) +2(x)(0)² + (0)³

= (x)³ + 0 + 0 + 0

= x³

10] ( (-1) + y) ³

= (-1)³ + 2(-1)²y + 2 (-1)y² + (y)³

= 1 + 2y - 2y² + y³