What is the factored form of the binomial expansion 81x^2 + 144xy + 64y^2?

(9x - 8y) ^2

(9x + 8y) ^2

(3x - 4y) ^2

(3x + 4y) ^2

(9x+8y) ^2

Step-by-step explanation:

81x^2 + 144xy + 64y^2

We recognize that this is a perfect square trinomial

perfect square trinomial is of the form: and factors to

(ax) 2 + 2abx + b2 = (ax + b) 2

(9x) ^2 + 2 * 9x * 8y + (8y) * 2 = (9x+8y) ^2

option b)

Step-by-step explanation:

a² + 2ab + b² = (a + b) ²

81x² = 9*9*x² = (9x) ²

64y² = 8*8*y² = (8y) ²

81x² + 144xy + 64y² = (9x) ² + 2 * 9x * 8y + (8y) ²

= (9x + 8y) ²