Question

Help me find the answers please! I don’t understand how to do it

Answer 1

(1)

Given Equation is x^2 + 4xy + 4y^2 - 9z^2

⇒ x^2 + 2xy + 2xy + 4y^2 - 9z^2

Add and subtract few terms,

⇒ x^2 + 2xy + 3xz - 3xz + 2xz - 2xz + 6yz - 6yz + 4y^2 - 9z^2

Rearrange the terms, we get

⇒ x^2 + 2xy + 3xz + 2xy + 4y^2 + 6yz - 3zx - 6yz - 9z^2

⇒ x(x + 2y + 3z) + 2y(x + 2y + 3z) - 3z(x + 2y + 3z)

⇒ (x + 2y + 3z)(x + 2y - 3z).

(2)

Given Equation is 16x^4 - y^4

⇒ (4x^2)^2 - (y^2)^2

We know that a^2 - b^2 = (a + b)(a - b)

⇒ (4x^2 + y^2)(4x^2 - y^2)

⇒ (4x^2 + y^2)[(2x^2)^2 - (y)^2]

⇒ (4x^2 + y^2)[(2x + y)(2x - y)]

⇒ (4x^2 + y^2)(2x + y)(2x - y)

(3)

Given Equation is 25(2x - y)^2 - 16(x - 2y)^2

⇒ [5(2x - y)]^2 - [4(x - 2y)]^2

We know that a^2 - b^2 = (a + b)(a - b)

⇒ [5(2x - y) + 4(x - 2y)][5(2x - y) - 4(x - 2y)]

⇒ [10x - 5y + 4x - 8y][10x - 5y - 4x + 8y]

⇒ [14x - 13y][6x + 3y]

⇒ 3(14x - 13y)(2x + y).

(4)

{x : x = 1/3^n, n ∈ R and 0 ≤ n ≤ 3}

Hope it helps!