Question

Expand:(3x+4y)(3x+5y)​

Answer 1

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$= (3x + 4x)(3x + 5y) \\ \\ = 3x(3x + 5y) + 4x(3x + 5y) \\ \\ = 9 {x}^{2} + 15xy + 12 {x}^{2} + 20xy \\ \\ = 9 {x}^{2} + 12 {x}^{2} + 15xy + 20xy \\ \\ = 21 {x}^{2} + 35y$

Answer 2

Answer:

Let us simplify the expression, we get

(3x + 4y) (3x + 5y) = (3x)2 + [(4y) + (5y)] 3x + [(4y) × (5y)]

By using the logic,

(x + a) (x + b) = x2 + (a + b)x + (a × b)

Here, x = 3x, a = 4y, b = 5y

Now, substitute the value we get

= 9x2 + [(9y) × (3x)] + 20y2

= 9x2 + 27xy + 20y2

∴ (3x + 4y) (3x + 5y) = 9x2 + 27xy + 20y2