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Q.

State if this statement is true or false.

‘The expression $a 2 + b c + a b + a c$ , can be expressed as a product of two binomials as $a + b a + c$ ’.

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a

True

b

False

answer is A.

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Detailed Solution

detailed_solution_thumbnail

The given expression is as follows,

a 2 + b c + a b + a c

.
It can be observed that there are four terms in the above expression. So, to factorize it, we first need to regroup the terms with common factors, and then we need to perform the factorization.
So, the given expression can be rearranged and grouped as follows.

a 2 + b c + a b + a c ⇔ a 2 + a b + a c + a b

Now, we need to factor out the highest common factor from each group to get the completely factored form of the expression as follows.

a a + b + c a + b = a + b a + c

So, it can be observed that we have got an expression which is actually a product of two binomial terms viz.,

a + b

and

a + c

.
Hence, the given statement is true.
The correct option is 1.

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