Question 318584
<pre><b>
F.  Multiply the FIRSTS   

{{{(red(2r)-3s)(red(5r)+7s)}}}     

Write that down:

{{{(2r)(5r)}}}

O. Multiply the OUTERS

{{{(red(2r)-3s)(5r+red(7s))}}}

{{{(2r)(7s)}}}

Write that down beside the {{{(2r)(5r)}}}

{{{(2r)(5r) + (2r)(7s)}}}


I. Multiply the INNERS

{{{(2r-red(3s))(red(5r)+7s)}}}

{{{(-3s)(5r)}}}

Write that down beside the {{{(2r)(5r) + (2r)(7s)}}}

{{{(2r)(5r) + (2r)(7s)+(-3s)(5r)}}}

L. Multiply the LASTS

{{{(2r-red(3s))(5r+red(7s))}}}

{{{(-3s)(7s)}}}

Write that down beside the {{{(2r)(5r) + (2r)(7s)+(-3s)(5r)}}}

{{{(2r)(5r) + (2r)(7s)+(-3s)(5r)+(-3s)(7s)}}}

Simplify

{{{10r^2+14rs-15rs-21s^2}}}

{{{10r^2-rs-21s^2}}}


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Multiply the red ones: {{{(red(h^2)+6h-7)(red(2h^2)+7h+10)}}}

{{{(h^2)(2h^2)}}}

Multiply the red ones: {{{(red(h^2)+6h-7)(2h^2+red(7h)+10)}}}

{{{(h^2)(2h^2)+(h^2)(7h)}}}

Multiply the red ones:  {{{(red(h^2)+6h-7)(2h^2+7h+red(10))}}}

{{{(h^2)(2h^2)+(h^2)(7h)+(h^2)(10)}}}

Multiply the red ones: {{{(h^2+red(6h)-7)(red(2h^2)+7h+10)}}}

{{{(h^2)(2h^2)+(h^2)(7h)+(h^2)(10)+(6h)(2h^2)}}}

Multiply the red ones: {{{(h^2+red(6h)-7)(2h^2+red(7h)+10)}}}

{{{(h^2)(2h^2)+(h^2)(7h)+(h^2)(10)+(6h)(2h^2)+(6h)(7h)}}}

Multiply the red ones: {{{(h^2+red(6h)-7)(2h^2+7h+red(10))}}}

{{{(h^2)(2h^2)+(h^2)(7h)+(h^2)(10)+(6h)(2h^2)+(6h)(7h)+(6h)(10)}}}

Multiply the red ones: {{{(h^2+6h-red(7))(red(2h^2)+7h+10)}}}

{{{(h^2)(2h^2)+(h^2)(7h)+(h^2)(10)+(6h)(2h^2)+(6h)(7h)+(6h)(10)+(-7)(2h^2)}}}

Multiply the red ones: {{{(h^2+6h-red(7))(2h^2+red(7h)+10)}}}

{{{(h^2)(2h^2)+(h^2)(7h)+(h^2)(10)+(6h)(2h^2)+(6h)(7h)+(6h)(10)+(-7)(2h^2)+(-7)(7h)}}}

Multiply the red ones: {{{(h^2+6h-red(7))(2h^2+7h+red(10))}}}

{{{(h^2)(2h^2)+(h^2)(7h)+(h^2)(10)+(6h)(2h^2)+(6h)(7h)+(6h)(10)+(-7)(2h^2)+(-7)(7h)+(-7)(10)}}}

Simplify:

{{{2h^4+7h^3+10h^2+12h^3+42h^2+60h-14h^2-49h-70}}}

{{{2h^4+19h^3+38h^2+11h-70}}}

Edwin</pre>