# Which is a factor of 6x^{2}y + 8x^{2} - 30y - 40?

x - 4, 3y + 4, x^{2} + 4, 3y - 5

**Solution:**

The given equation is

6x^{2}y + 8x^{2} - 30y - 40

Rearranging the equation we get

= 6x^{2}y - 30y + 8x^{2} - 40

= y(6x^{2} - 30) + 8(x^{2} - 5)

= 6y(x^{2} - 5) + 8(x^{2} - 5)

= (x^{2} - 5)(6y + 8)

= 2(x^{2} - 5)(3y + 4)

Hence the factors of the given equation are:

2, (x^{2} - 5) and (3y + 4)

Another example of identifying factors can be identifying factors of:: 4a^{2} + b^{2} - c^{2} + 4ab

= 4a^{2} + b^{2} - c^{2} + 4ab

= 4a^{2} + 4ab + b^{2} - c^{2}

= (4a^{2} + 4ab + b^{2}) - c^{2}

= (2a + b)^{2} - c^{2} --- (1)

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

In equation (1)

(2a + b)^{2} = a^{2} and c^{2} = b^{2},

Therefore (1) can be rewritten as (2a + b)^{2} - c^{2} = (2a + b + c)(2a + b - c)

Hence the factors of 4a^{2} + b^{2} - c^{2} + 4ab are (2a + b + c)(2a + b - c)

## Which is a factor of 6x^{2}y + 8x^{2} - 30y - 40?

x - 4, 3y + 4, x^{2} + 4, 3y - 5

**Summary:**

3y + 4 is a factor of 6x^{2}y + 8x^{2} - 30y - 40

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