(х+а)(х+б)=х²+(а+б)х+аб

The equation you provided, \((x+a)(x+b) = x^2 + (a+b)x + ab\), represents the factorization of a quadratic expression.

To understand why this is true, let's expand the left-hand side:

1. Start with \((x + a)(x + b)\).
2. Distribute \(x\) across both terms in the second parenthesis: \[ x \cdot x + x \cdot b + a \cdot x + a \cdot b \] This simplifies to: \[ x^2 + bx + ax + ab \]
3. Combine the like terms \((bx + ax)\): \[ x^2 + (a+b)x + ab \]

Thus, we've shown that \((x + a)(x + b)\) expands to \(x^2 + (a + b)x + ab\), confirming the original equation is correct. This identity can be useful in factoring quadratic equations and solving quadratic equations by recognizing the roots.