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

Question

Is equality correct?

(b3)(b+7)=b2+4b21 (b-3)(b+7)=b^2+4b-21

Video Solution

Step-by-Step Solution

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

(b3)(b+7) (b-3)(b+7)

Applying the distributive property (FOIL), we have:

  • First: b×b=b2 b \times b = b^2
  • Outer: b×7=7b b \times 7 = 7b
  • Inner: 3×b=3b -3 \times b = -3b
  • Last: 3×7=21 -3 \times 7 = -21

Combine these terms:

b2+7b3b21 b^2 + 7b - 3b - 21

Simplify by combining like terms:

b2+(7b3b)21=b2+4b21 b^2 + (7b - 3b) - 21 = b^2 + 4b - 21

The expression on the left simplifies to b2+4b21 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.

Answer

Yes