Rewriting Expressions: Standard Form and Difference of Two Squares

This lesson covers how to rewrite expressions as trinomials in standard form or as a difference of two squares by examining their structure. It explains the components of a quadratic expression, addresses common misunderstandings, and provides techniques for rewriting expressions. Advanced examples illustrate these concepts further.

What is the standard form of a quadratic expression?

• ax^2 + bx + c

• bx^2 + ax + c

• ax + bx^2 + c

• ax^2 + c

Which of the following is a difference of two squares?

• x^2 + 4

• x^2 - 7

• x^2 - 4

• x^2 + 7

What must be true for an expression to be a difference of two squares?

• The constant term must be positive

• The expression must have a linear term

• The quadratic term must be zero

• Both terms must be perfect squares

How can you rewrite 6x - 3x^2 + 2 in standard form?

• 3x^2 - 6x + 2

• -3x^2 + 6x + 2

• -6x^2 + 3x + 2

• 6x^2 - 3x + 2

What is the result of substituting y^3 for y in the expression 5y^2 - 4y + 1?

• 5y^3 - 4y + 1

• 5y^6 - 4y^3 + 1

• 5y^6 - 4y^2 + 1

• 5y^3 - 4y^2 + 1

Which expression is a difference of two squares with two variables?

• x^3 + 2y

• x^3 - 2y

• x^6 + 4y^2

• x^6 - 4y^2

What is the perfect square form of x^4 - 9?

• (x^2)^2 - 3^2

• (x^3)^2 + 3^2

• (x^2)^2 + 3^2

• (x^3)^2 - 3^2