How do you find the product #(g+5h)^2#?

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Answer 1 · 2017-01-16T03:33:49

See the full solution process below:

First, we transform this expression to:

#(g + 5h)^2 = (g + 5h)(g + 5h)#

Now, to multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

#(color(red)(g) + color(red)(5h))(color(blue)(g) + color(blue)(5h))# becomes:

#(color(red)(g) xx color(blue)(g)) + (color(red)(g) xx color(blue)(5h)) + (color(red)(5h) xx color(blue)(g)) + (color(red)(5h) xx color(blue)(5h))#

#g^2 + 5gh + 5gh + 25h^2#

We can now combine like terms:

#g^2 + (5 + 5)gh + 25h^2#

#g^2 + 10gh + 25h^2#