1.

Factorise 8(a+1)^2+2(a+1)(b+2)-15(b+2)^2

Answer»

\bf\,8(a+1)^2+2(a+1)(b+2)-15(b+2)^2

=8m^2+2mn-15n^2    \text{ wherre m=a+1 and n=b+2}

\textbf{Using middle term factorization}

=8m^2+12mn-10mn-15n^2

=4m(2m+3n)-5n(2m+3n)

=(2m+3n)(4m-5n)

=(2(a+1)+3(b+2))(4(a+1)-5(b+2))

=(2a+2+3b+6)(4a+4-5b-10)

=(2a+3b+8)(4a-5b-6)

\therefore\bf\,8(a+1)^2+2(a+1)(b+2)-15(b+2)^2=(2a+3b+8)(4a-5b-6)


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