Find a value for m and n to make a true statement.

a) mx^2 - 36 = (3x + 6) (3x - 6)

b) (mx + ny) ^2 = 4x^2 + 12xy + 9y^2

Correct answer: a) m = 9; b) m = 2 and n = 3

Step-by-step explanation:

Given:

a) m x² - 36 = (3 x + 6) (3 x - 6) ⇒ m = ?

b) (m x + n y) ² = 4 x² + 12 x y + 9 y² ⇒ m, n = ?

a) m x² - 36 (3 x + 6) (3 x - 6)

The right side of the equation is the difference of the square, so we will present the left side in the same way:

(√m x) ² - 6² = (3 x + 6) (3 x - 6)

(√m x + 6) (√m x - 6) = (3 x + 6) (3 x - 6)

√m = 3 / ² when we square both sides of the equation we get:

m = 9

b)

(m x + n y) ² = 4 x² + 12 x y + 9 y²

The left side of the equation is the complete square of the binomial, so we will present the right side in the same way:

(m x + n y) ² = (2 x) ² + 2 · 2 x · 3 y + (3 y) ² = (2 x + 3 y) ²

(m x + n y) ² = (2 x + 3 y) ² ⇒

m = 2 and n = 3

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