Question

factorise (9y*+25z*+15yz)
​

Answer 1

Step-by-step explanation:

Since we have given that

4x^2+9y^2-25x^2+12xy4x

2

+9y

2

−25x

2

+12xy

We need to find the factorisation:

\begin{gathered}(4x^2+9y^2+12xy)-25z^2\\\\Using\ (a+b)^2=a^2+b^2+2ab\\\\=(2x)^2+(3y)^2+2\times 2x\times 3y-(5z)^2\\\\=(2x+3y)^2-(5z)^2\\\\Using\ a^2-b^2=(a-b)(a+b)\\\\=(2x+3y-5z)(2x+3y+5z)\end{gathered}

(4x

2

+9y

2

+12xy)−25z

2

Using (a+b)

2

=a

2

+b

2

+2ab

=(2x)

2

+(3y)

2

+2×2x×3y−(5z)

2

=(2x+3y)

2

−(5z)

2

Using a

2

−b

2

=(a−b)(a+b)

=(2x+3y−5z)(2x+3y+5z)