Match Each Quadratic Expression Written As A Product With Its Equivalent Expanded Expression:A. { (x+4)(x+5)$}$ 1. ${ 2x^2 + 16x + 24\$} B. { (2x+3)(x+8)$}$ 2. { X^2 + 9x + 20$}$ C. { (x+10)(x+2)$}$
Introduction
Quadratic expressions are a fundamental concept in algebra, and being able to expand them is a crucial skill for any math enthusiast. In this article, we will explore how to match each quadratic expression written as a product with its equivalent expanded expression. We will break down each expression into its individual components and provide a step-by-step guide on how to expand them.
A. Expanding {(x+4)(x+5)$}$
To expand the expression {(x+4)(x+5)$}$, we need to multiply each term in the first expression by each term in the second expression.
Step 1: Multiply the first term in the first expression by each term in the second expression
- {x \cdot x = x^2$
- [$x \cdot 5 = 5x$
- [$4 \cdot x = 4x$
- [$4 \cdot 5 = 20$
Step 2: Combine like terms
- [$x^2 + 5x + 4x + 20$
- [$x^2 + 9x + 20$
Therefore, the expanded expression of [(x+4)(x+5)\$} is {x^2 + 9x + 20$].
B. Expanding [(2x+3)(x+8)\$}
To expand the expression {(2x+3)(x+8)$}$, we need to multiply each term in the first expression by each term in the second expression.
Step 1: Multiply the first term in the first expression by each term in the second expression
- ${$2x \cdot x = 2x^2$
- [$2x \cdot 8 = 16x$
- [$3 \cdot x = 3x$
- [$3 \cdot 8 = 24$
Step 2: Combine like terms
- [$2x^2 + 16x + 3x + 24$
- [$2x^2 + 19x + 24$
Therefore, the expanded expression of [(2x+3)(x+8)\$} is ${$2x^2 + 19x + 24$].
C. Expanding [(x+10)(x+2)\$}
To expand the expression {(x+10)(x+2)$}$, we need to multiply each term in the first expression by each term in the second expression.
Step 1: Multiply the first term in the first expression by each term in the second expression
- {x \cdot x = x^2$
- [$x \cdot 2 = 2x$
- [$10 \cdot x = 10x$
- [$10 \cdot 2 = 20$
Step 2: Combine like terms
- [$x^2 + 2x + 10x + 20$
- [$x^2 + 12x + 20$
Therefore, the expanded expression of [(x+10)(x+2)\$} is [$x^2 + 12x + 20$].
Conclusion
In conclusion, expanding quadratic expressions is a crucial skill for any math enthusiast. By following the step-by-step guide provided in this article, you should be able to match each quadratic expression written as a product with its equivalent expanded expression. Remember to multiply each term in the first expression by each term in the second expression and then combine like terms to get the final expanded expression.
Frequently Asked Questions
Q: What is a quadratic expression?
A: A quadratic expression is a polynomial expression of degree two, which means the highest power of the variable is two.
Q: How do I expand a quadratic expression?
A: To expand a quadratic expression, you need to multiply each term in the first expression by each term in the second expression and then combine like terms.
Q: What is the difference between a quadratic expression and a quadratic equation?
A: A quadratic expression is a polynomial expression of degree two, while a quadratic equation is a quadratic expression set equal to zero.
Additional Resources
For more information on expanding quadratic expressions, check out the following resources:
- Khan Academy: Expanding Quadratic Expressions
- Mathway: Expanding Quadratic Expressions
- Wolfram Alpha: Expanding Quadratic Expressions
Introduction
Quadratic expressions are a fundamental concept in algebra, and being able to expand and manipulate them is a crucial skill for any math enthusiast. In this article, we will provide a comprehensive Q&A guide on quadratic expressions, covering topics such as expanding, factoring, and solving quadratic equations.
Q: What is a quadratic expression?
A: A quadratic expression is a polynomial expression of degree two, which means the highest power of the variable is two. It is typically written in the form of ax^2 + bx + c, where a, b, and c are constants.
Q: How do I expand a quadratic expression?
A: To expand a quadratic expression, you need to multiply each term in the first expression by each term in the second expression and then combine like terms. For example, to expand the expression (x+4)(x+5), you would multiply each term in the first expression by each term in the second expression and then combine like terms.
Q: What is the difference between a quadratic expression and a quadratic equation?
A: A quadratic expression is a polynomial expression of degree two, while a quadratic equation is a quadratic expression set equal to zero. For example, the expression x^2 + 4x + 4 is a quadratic expression, while the equation x^2 + 4x + 4 = 0 is a quadratic equation.
Q: How do I factor a quadratic expression?
A: To factor a quadratic expression, you need to find two binomials whose product is equal to the original expression. For example, to factor the expression x^2 + 6x + 8, you would look for two binomials whose product is equal to the original expression and then combine them.
Q: What is the formula for the product of two binomials?
A: The formula for the product of two binomials is (a+b)(c+d) = ac + ad + bc + bd.
Q: How do I solve a quadratic equation?
A: To solve a quadratic equation, you can use the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / 2a. You can also use factoring or the quadratic formula to solve quadratic equations.
Q: What is the quadratic formula?
A: The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are constants.
Q: How do I use the quadratic formula to solve a quadratic equation?
A: To use the quadratic formula to solve a quadratic equation, you need to plug in the values of a, b, and c into the formula and then simplify the expression.
Q: What is the difference between a quadratic equation and a linear equation?
A: A quadratic equation is a quadratic expression set equal to zero, while a linear equation is a linear expression set equal to zero.
Q: How do I graph a quadratic equation?
A: To graph a quadratic equation, you can use the x-intercepts and the vertex of the parabola to plot the graph.
Q: What is the vertex of a parabola?
A: The vertex of a parabola is the point on the parabola that is the lowest or highest point.
Q: How do I find the x-intercepts of a parabola?
A: To find the x-intercepts of a parabola, you can set the equation equal to zero and then solve for x.
Q: What is the axis of symmetry of a parabola?
A: The axis of symmetry of a parabola is the vertical line that passes through the vertex of the parabola.
Conclusion
In conclusion, quadratic expressions are a fundamental concept in algebra, and being able to expand, factor, and solve quadratic equations is a crucial skill for any math enthusiast. By following the Q&A guide provided in this article, you should be able to master the skill of working with quadratic expressions and become a math whiz!
Frequently Asked Questions
Q: What is a quadratic expression?
A: A quadratic expression is a polynomial expression of degree two, which means the highest power of the variable is two.
Q: How do I expand a quadratic expression?
A: To expand a quadratic expression, you need to multiply each term in the first expression by each term in the second expression and then combine like terms.
Q: What is the difference between a quadratic expression and a quadratic equation?
A: A quadratic expression is a polynomial expression of degree two, while a quadratic equation is a quadratic expression set equal to zero.
Additional Resources
For more information on quadratic expressions, check out the following resources:
- Khan Academy: Quadratic Expressions
- Mathway: Quadratic Expressions
- Wolfram Alpha: Quadratic Expressions
By following the Q&A guide provided in this article and practicing with the resources listed above, you should be able to master the skill of working with quadratic expressions and become a math whiz!