Multiplying binomials by polynomials challenge | Algebra I | High School Math | Khan Academy

TL;DR

Determine the values of A and B in the quadratic equation by expanding and matching terms.

Transcript

• [Voiceover] So we've got the expression two X plus four times five X minus nine is equal to AX squared plus BX minus 36. And what we want to figure out is what are A and B going to be? And I encourage you to pause the video and try to figure it out. Well there's a coupe of ways of trying to tackle it and the most straightforward would be just let... Read More

Key Insights

• 💁 The quadratic equation can be simplified and matched to its expanded form to determine the values of A and B.
• 🍉 Expanding the binomials in the equation helps in visualizing and simplifying the terms.
• 🍉 The coefficient of the X^2 term in the quadratic equation is crucial in finding the value of A.
• 🙃 By comparing and matching the terms on both sides of the equation, we can deduce the values of A and B.
• 🙃 The constant term must be multiplied to obtain the expected value on both sides of the equation.
• ❓ There are multiple approaches to solve the problem, but careful consideration and simplification are necessary.
• 🍉 Identifying and understanding the various terms in the equation are essential steps in finding the values of A and B.

Questions & Answers

Q: How can we determine the values of A and B in the quadratic equation?

To find the values of A and B, we can expand and simplify the left-hand side of the equation by distributing the two binomials. By matching the terms and coefficients, we can identify the values of A and B.

Q: What is the significance of the term AX^2 in the equation?

The term AX^2 represents the coefficient of the second-degree term in the quadratic equation. In this case, it is essential to determine the value of A to fully define the equation.

Q: What are the possible ways to approach the problem?

One approach is to expand the left-hand side of the equation by distributing the binomials and then matching the terms. Another approach involves considering how to obtain an X^2 term, followed by an X term, and finally, a constant term.

Q: Can we simplify the equation further?

After expanding and simplifying the left-hand side of the equation, we end up with 10X^2 + 2X - 36. This cannot be simplified further, as we have identified the values of A and B.

Summary & Key Takeaways

• The goal is to find the values of A and B in the equation AX^2 + BX - 36 by expanding and matching terms.

• By distributing two binomials on the left-hand side of the equation, we can match the terms and coefficients.

• After simplifying, it is found that A = 10 and B = 2.