Question

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

Answer 1

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

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

$\textbf{Using middle term factorization}$

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

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

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

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

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

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

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

Answer 2

8(a+1)  

2

+2(a+1)(b+2)−15(b+2)  

2

 

Let a+1=x and b+2=y. Then,

8x  

2

+2xy−15y  

2

 

=8x  

2

+12xy−10xy−15y  

2

 

=4x(2x+3y)−5y(2x+3y)

=(2x+3y)(4x−5y)

=(2a+3b+8)(4a−5b−6)