Question

factorise 9a^2+49b^2+c^2-42ab+14bc-6ac

Answer 1

it is I'm the form (a+b+c)^2 =>
a^2+b^2+c^2+2ab+2bc+2ca
=> (-3a)^2 + (7b)^2 + c^2 + 2(-3a)(7b) + 2(7b)(c)
+ 2(c)(-3a)
=> (-3+7b+c)^2
please mark as brainliest

Answer 2

Given,

An algebraic expression: 9a^2+49b^2+c^2-42ab+14bc-6ac

To find,

The factorized product of the given algebraic expression.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

If x, y, and z are three variables, then there exists an algebraic identity such that,

(x+y+z)^2 = x^2 + y^2 + z^2 + 2(xy + yz + zx)

{Statement-1}

Now, according to the question;

On simplifying and factorizing the given algebraic expression, we get;

9a^2+49b^2+c^2-42ab+14bc-6ac

= (3a)^2 + (7b)^2 + (c)^2 + 2{-21ab + 7bc - 3ac}

= (-3a)^2 + (7b)^2 + (c)^2 + 2{(-3a)(7b) + (7b)(c) + (-3a)(c)}

= (-3a + 7b + c)^2

{according to statement-1}

= (-3a + 7b + c)(-3a + 7b + c)

Hence, the factorized product of the given algebraic expression is equal to (-3a + 7b + c)(-3a + 7b + c).