contestada

Consider the polynomial identity: (x+y) ^3 = x^3 +3x^2y + 3xy^2 +y ^3

(a) prove this identity by expanding the left - hand side of the equation.

(b) use your calculator to find the value of 11^3 then use the identity to show the same result. Carefully consider your choice of a and b

Respuesta :

Step-by-step explanation:

Polynomial identity: [tex](x+y)^{3} = x^{3} + y^{3} + 3x^{2}y + 3xy^{2}[/tex]

(A) Expanding above identity by LHS:

[tex](x+y)^{3}\\(x+y)(x+y)(x+y)\\(x+y)(x^{2}+2xy+y^{2})\\(x^{3}+2x^{2}y+y^{2}x+x^{2}y+2xy^{2}+y^{3})\\(x^{3}+3y^{2}x+3xy^{2}+y^{3})[/tex] Hence , proved.

(B) Value of ,  [tex]11^{3} = 11(11)(11) = 121(11) = 1331[/tex]. Finding the same with help of equation:

[tex]11^{3} = (10+1)^{3}\\11^{3} = 10^{3} + 3(1^{2})10+3(1)(10^{2})+1^{3}\\11^{3} = 1000 + 30 + 300 + 1\\11^{3} = 1331[/tex] Hence , Both produce same result.

Otras preguntas