Question

5. Factorise:
( 4x^2+9y^2+16z^2+12xy-24yz-16xz​

Answer 1

Answer:

4x²+9y²+16z²+12xy-24yz-16xz

= (2x)²+(3y)²+(4z)²+12xy-24yz-16xz

= (2x)²+(3y)²+(-4z)²+12xy-24yz-16xz

= (2x)2+(3y)²+(-42)²+ 2(2x)(3y)+2(3y)(-4z)+2(2x)(-4z)

Using (a + b + c) = a + b2+ &' + 2ab + 2bc + 2ac

Putting a = 2x, b=3y,c=-4z

= (2x + 3y - 4z)²

Answer 2

Answer:

★question :-

† factorise

4x^2+9y^2+16z^2+12xy-24yz-16xz

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● Identity

An identity is an equality which is true find all

values of a variable in the equality .

In an identity the right hand side expression is called expanded form of the left hand side expression.

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Now comparing that with the identity

⟹ (a^2+b^2+b^2) =2ab+2bc+2ac

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† Solution :-

We can we write the given expression -

Now we get :

4x^2+9y^2+16z^2+12xy-24yz-16xz

: ⟹2x^2+3y^2+4z^2+2×2x×3y+2×3y+

(-4z)+2×2x×(-4z)

: ⟹ [ 2x+3y+(-4z)]^2

: ⟹[ 2x+3y-4z] [ 2x+3y-4z]

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Required Answer :

⟹ ( 2x+3y-4z) ( 2x+3y-4z)

★ Identity used :

[(a^2+b^2+c^2) =2ab+2bc+2ac]

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I hope this is helpful.....