How do you simplify #8( p + q ) ^ { 2} - 6( p ^ { 2} - q ^ { 2} ) - 9( p - q ) ^ { 2}#?

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Answer 1 · 2017-06-29T05:58:45

Let #(p+q)=x and (p-q)=y#

Then the given expression becomes

#8x^2-6xy-9y^2#

#=>8x^2-12xy+6xy-9y^2#

#=>4x(2x-3y)+3y(2x-3y)#

#=>(4x+3y)(2x-3y)#

#=>(4(p+q)+3(p-q))(2(p+q)-3(p-q))#

#=>(4p+4q+3p-3q)(2p+2q-3p+3q)#

#=>(7p+q))(5q-p)#

#=>5q^2+34pq-7p^2#