Question 1151532
What are the terms of the 2 factors of the
binomial so that the Inner and Outer products
add up to the middle term?
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{{{ ( 5w + a )*( w + b ) }}}
Note that {{{ a*b = 0 }}} since the 3rd term is {{{ 0 }}}
so, either {{{ a }}} or {{{ b }}} is zero
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I'll try {{{ a=0 }}}
{{{ ( 5w + 0 )*( w + b ) = 5w^2 + 0*w + 5*b*w + 0*b }}}
{{{ b = 6/5 }}} 
{{{ ( 5w + 0 )*( w + 6/5 ) }}} gives the correct answer
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I'll try {{{ b = 0 }}}
{{{ ( 5w + a )*( w + 0 ) }}}
{{{ 5w^2 + a*w + 0*5w + 0*a }}}
{{{ a = 6 }}}
{{{ ( 5w + 6 )*( w + 0 ) }}} gives the correct answer
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{{{ 5w*( w + 6/5 ) }}}
{{{ w*( 5w + 6 ) }}} 
both are correct answers
The 2nd one is the usual answer