$$ (7+8)^2=\text{?} $$

$$ 7^2+2\times7\times8+8^2 $$

$$ 7^2-2\times7\times8+8^2 $$

Fill in the blanks:$$ (x+?)^2=x^2+?+25 $$

$$ \sqrt{125},\sqrt{125}x $$

The formula for the sum of squares

$(X + Y)2=X2+ 2XY + Y2$

This formula is one of the shortcut formulas and it describes the square sum of two numbers.

That is, when we encounter two numbers with a plus sign (sum) and they are between parentheses and raised as an expression to the square, we can use this formula.
Pay attention - The formula also works for non-algebraic expressions or combined combinations with numbers and unknowns.
It's good to know that it is very similar to the formula for the difference of squares and differs only in the minus sign of the central element.

Detailed explanation

Start practice

Test yourself on the sum of squares formula!

Choose the expression that has the same value as the following:

$$ (x+y)^2 $$

Practice more now

Let's look at an example

$(X+9)^2=$
Here we identify two elements between which is the plus sign and they are within parentheses and raised to the square as a single expression.
Therefore, we can use the formula for the sum of squares.
We will work according to the formula and pay attention to the minus and plus signs.
We obtain:
$(X+9)^2=x^2+18x+81$
Indeed, we pronounce the same expression differently using the formula.