Verify the Polynomial Equality: (b-3)(b+7) = b²+4b-21

Is equality correct?

$(b-3)(b+7)=b^2+4b-21$

To solve this problem, let's expand and simplify the expression on the left-hand side:

$(b-3)(b+7)$

Applying the distributive property (FOIL), we have:

• First: $b \times b = b^2$
• Outer: $b \times 7 = 7b$
• Inner: $-3 \times b = -3b$
• Last: $-3 \times 7 = -21$

Combine these terms:

$b^2 + 7b - 3b - 21$

Simplify by combining like terms:

$b^2 + (7b - 3b) - 21 = b^2 + 4b - 21$

The expression on the left simplifies to $b^2 + 4b - 21$. This is identical to the expression on the right-hand side of the equality.

Since both sides of the equation are equal, the given equality is correct.

Thus, the correct answer is Yes.