Question

why is 2+2=4
and 2×2=4
explain why answers are same
​

Answer 1

We use the concept of equations here.

If the product of a number by itself is equal to the sum of a number by itself,

$\hookrightarrow x\times x=x^{2}$

$\hookrightarrow x+x=2x$

Since two are equal, we are left with the equation below,

$\hookrightarrow x^{2}=2x$

We can subtract the same number from both sides of an equation.

$\hookrightarrow x^{2}-2x=2x-2x$

$\hookrightarrow x^{2}-2x=0$

This kind of equation has the highest degree of 2, so it is called a quadratic equation. To solve this, we need to know about factorization.

Factorization is the opposite process of expansion. (Simply, it is the method of showing the expression as the product of factors.)

To get the factorization, let's try $x(x-2)$. (We use 'polynomial identity' which we learn in a higher class, but here we will skip the concept.)

$\hookrightarrow x(x-2)=x\times x-x\times2$

$\hookrightarrow x(x-2)=x^{2}-2x$

So, the factorization is $x(x-2)$.

Now, we are given that,

$\hookrightarrow x(x-2)=0$

For the product to be zero, each factor can be zero. Now we can solve the following simple equations,

$\hookrightarrow x=0\text{ or }x-2=0$

$x=0\text{ or }x=2$ satisfies the equation. So, the reason for the same answer is explained.

And this also gives another result, $0\times0=0$ and $0+0=0$, which may seem obvious but we solved it by using the concept of equations. Let's end the answer here.

Answer 2

Answer:

We use the concept of equations here.

If the product of a number by itself is equal to the sum of a number by itself,

$\hookrightarrow x\times x=x^{2}$

$\hookrightarrow x+x=2x$

Since two are equal, we are left with the equation below,

$\hookrightarrow x^{2}=2x$

We can subtract the same number from both sides of an equation.

$\hookrightarrow x^{2}-2x=2x-2x$

$\hookrightarrow x^{2}-2x=0$

This kind of equation has the highest degree of 2, so it is called a quadratic equation. To solve this, we need to know about factorization.

Factorization is the opposite process of expansion. (Simply, it is the method of showing the expression as the product of factors.)

To get the factorization, let's try $x(x-2)$. (We use 'polynomial identity' which we learn in a higher class, but here we will skip the concept.)

$\hookrightarrow x(x-2)=x\times x-x\times2$

$\hookrightarrow x(x-2)=x^{2}-2x$

So, the factorization is $x(x-2)$.

Now, we are given that,

$\hookrightarrow x(x-2)=0$

For the product to be zero, each factor can be zero. Now we can solve the following simple equations,

$\hookrightarrow x=0\text{ or }x-2=0$

$x=0\text{ or }x=2$ satisfies the equation. So, the reason for the same answer is explained.

And this also gives another result, $0\times0=0$ and $0+0=0$, which may seem obvious but we solved it by using the concept of equations. Let's end the answer here.