Question

Ans both questions asap

Answer 1

Your answer is here I hope correct answer

Answer 2

(1)

Given a + b + c = 15 and ab + bc + ca = 15.

We need to find (a + b)^3 + (b + c)^3 + (a + c)^3 - 3(a + b)(b + c)(a + c).

= > a^3 + b^3 + 3ab(a + b) + b^3 + c^3 + 3bc(b + c) + a^3 + c^3 + 3ac(a + c) - (3a^2b + 6abc + 3a^2c + 3ac^2 + 3ab^2 + 3b^2c + 3bc^2)

= > a^3 + b^3 + 3a^2b + 3ab^2 + b^3 + c^3 + 3b^2c + 3bc^2 + a^3 + c^3 + 3a^2c + 3ac^2 - 3a^2b - 6abc - 3a^2c - 3ac^2 - 3ab^2 - 3b^2c - 3bc^2

= > 2a^3 + 2b^3 + 2c^3 - 6abc

= > 2(a^3 + b^3 + c^3 - 3abc)

= > 2(a + b + c)[(a^2 + b^2 + c^2) - (ab + bc + ca)]

= > 2(5)[(a^2 + b^2 + c^2) - (15)]

We know that a^2 + b^2 + c^2 = (a + b + c)^2 - 2(ab + bc + ca)

On substituting we get,

= > 2(5)[(a + b + c)^2 - 2(ab + bc + ca) - 15]

= > 10[(5)^2 - 2(15) - 15]

= > 10(25 - 30 - 15)

= > 10(-20)

= > -200.



The value of (a + b)^3 + (b + c)^3 + (a + c)^3 - 3(a + b)(b + c)(c + a) = -200



(2)

Given Equation is a^12y^4 - a^4y^12

= > a^4y^4(a^8 - y^8)

= > a^4y^4((a^4)^2 - (y^4)^2)

= > a^4y^4((a^4 + y^4)(a^4 - y^4))

= > a^4y^4((a^4 + y^4)(a^2)^2 - (y^2)^2))

= > a^4y^4(a^4 + y^4)(a^2 + y^2)(a^2 - y^2)

= > a^4y^4(a^4 + y^4)(a^2 + y^2)(a + y)(a - y)



Hope this helps!