Question

(a+b)square - (a-b) square=?
a) 2ab
b) 4ab
c) 2(a square + b square )
d) 2a square -2b square
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Answer 1

Answer:

I know the answer is = 4ab, but if I could explain it…

Use the perfect square formula for each of the two expressions (a + b )² = a² + 2ab + b²

So, (a+b)² becomes a² + 2ab + b²

And, (a-b)² becomes a² - 2ab + b²

Since we are simplifying we use the distributive property method. So distribute the parentheses () in one of the expressions.

Don’t forget we are subtracting -,

thus we have the expression, a² + 2ab + b² - (a² - 2ab + b²)

Distribute the - sign in the parentheses ().

Group like terms - a² +a² + 2ab + 2ab -b²+b²

Cancel out -a²+a² and -b²+b²

Therefore∴ , 2ab + 2ab = 4ab

Answer 2

Answer:

b)4ab

We know,

ab=(a+b devided 2) sqare -(a-b devided 2)sqare

so,4ab= (a+b) sqare-(a-b) sqare