Question

(х+4у)^2 - (4у-х)(х+4у)

Answer 1

(х+4у)^2 - (4y-x)(4y+x) = (x^2+8xy+16y^2) - (16y^2-x^2) = (x^2+8xy+16y^2) - -16y^2+x^2 = x^2+x^2+8xy = 2x^2+8xy

Answer 2

To simplify the expression (х+4у)^2 - (4у-х)(х+4у), you can use the distributive property (also known as the FOIL method) to expand the squares and then combine like terms:

(х+4у)^2 - (4у-х)(х+4у)

First, expand (х+4у)^2:

(х+4у)^2 = (х+4у)(х+4у) = х(х+4у) + 4у(х+4у)

Now, expand (4у-х)(х+4у) using the distributive property:

(4у-х)(х+4у) = 4у(х+4у) - х(х+4у)

Now, substitute these expanded expressions back into the original equation:

х(х+4у) + 4у(х+4у) - (4у(х+4у) - х(х+4у))

Now, distribute the terms inside the parentheses:

х^2 + 4ух + 4ух + 16у^2 - (4ух + 16у^2 - х^2 - 4ух)

Now, simplify by combining like terms:

х^2 + 4ух + 4ух + 16у^2 - 4ух - 16у^2 + х^2 + 4ух

Notice that many terms cancel each other out:

4ух and -4ух cancel out. 16у^2 and -16у^2 cancel out. х^2 and -х^2 cancel out.

You are left with:

8ух + 8ух

Now, combine like terms:

8ух + 8ух = 16ух

So, the simplified expression is:

16ух