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Choose the correct option which represents the product of the expression $4 a + 5 b × 5 a − 6 b$ .

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20 a 2 + a b − 30 b 2

20 a 2 − a b − 30 b 2

20 a 2 − a b + 30 b 2

None of these

answer is A.

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Detailed Solution

The given algebraic expression is

4 a + 5 b × 5 a − 6 b

.
Mathematically, the distributive property can be represented for three numbers a, b and c as follows,

a × (b + c) = (a × b) + (a × c)

To find the product, we apply the distributive property of multiplication,

(4 a + 5 b) × (5 a − 6 b) = 4 a (5 a − 6 b) + 5 b (5 a − 6 b) = 4 a (5 a) + 4 a (− 6 b) + 5 b (5 a) + 5 b (− 6 b) = 20 a 2 − 24 a b + 25 a b − 30 b 2

Now, we will simplify the above expression by adding the like terms together to get the required product as follows,

20 a 2 + a b − 30 b 2

The required product of the expression is

20 a 2 + a b − 30 b 2

.
Hence, the correct option is (1).

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