Question

(x+2y)³ + ( 2x + y)³show the full process with the identity a³+b³= (a +b) ( a² -ab+ b²)​

Answer 1

Step-by-step explanation:

(x+2y)³ + (2x+y)³

• let (x+2y) be "a"
• (2x+y) be "b"

so using the above formulae in the question

we will calculate the value

• a³+b³= (a+b) (a²-ab+b²)
• (x+2y)³ + (2x+y)³

= [(x+2y)+(2x+y)] [(x+2y)² - (x+2y X 2x+y) + (2x+y)²]

=[(3x+3y)] [(x²+4y²+4xy)-(2x²+xy+4xy+2y²)+(4x²+y²+4xy)]

=[3x+3y] [(5x²-2x²)+(5y²-2y²)+(-8xy+5xy)

=[3x+3y] [3x²+3y²-3xy]

=3[x+y] [x²+y²-xy]

hence we have got same as it is in the formulae

Answer 2

Answer:

$(x+2y)^{3} + (2x+y)^{3}\\\\=(x+2y)([x]^{2}-[x][2y]+[2y]^{2})+(2x+y)([2x]^{2}-[2x][y]+[y]^{2})\\\\=(x+2y)(x^{2}-2xy+4y^{2})+(2x+y)(4x^{2}-2xy+y^{2})\\\\=[x^{3}-2x^{2}y+4xy^{2} + 2x^{2}y-4xy^{2}+8y^{3}]+\\[8x^{3}-4x^{2}y+2xy^{2} + 4x^{2}y-2xy^{2}+y^{3}]\\=[x^{3}-2x^{2}y + 2x^{2}y+4xy^{2}-4xy^{2}+8y^{3}]+\\[8x^{3}-4x^{2}y + 4x^{2}y+2xy^{2}-2xy^{2}+y^{3}]\\\\=[x^{3}}+8y^{3}]+[8x^{3}}+y^{3}]\\=x^{3}}+8y^{3}+8x^{3}}+y^{3}\\=x^{3}}+8x^{3}+8y^{3}+y^{3}\\=9x^{3}+9y^{3}$

Step-by-step explanation: