Question

Factorise the expression: $9x^2+24xy+16y^2-25z^2$

• A. (3x+4y+5z)(3x+4y+5z)
• B. (3x+4y-5z)(3x+4y-5z)
• C. (3x+4y-5z)(3x+4y+5z)
• D. (3x4y-5z)(3x-4y+5z)

Answer 1

The correct option is C (3x+4y-5z)(3x+4y+5z)

The given expression is $9x^2+24xy+16y^2-25z^2$

= $9x^2+24xy+16y^2-25z^2$
= $(3x{)}^2+2(3x\left)\right(4y)+(4y{)}^2-(5z{)}^2$
= $(3x+4y{)}^2-(5z{)}^2$
= $\left[\right(3x+4y)-5z]\left[\right(3x+4y)+5z]$
= $(3x+4y-5z)(3x+4y+5z$