Louisiana LEAP 2025 Algebra I: a complete guide to expressions and structure (A-SSE, A-APR, N-RN, N-Q)

What this module covers

This guide covers expressions and structure on the Louisiana LEAP 2025 Algebra I test: interpreting the parts of an expression (A-SSE.A.1), rewriting and factoring quadratics (A-SSE.B.3), polynomial operations (A-APR.A.1), the exponent rules and rational exponents (N-RN), and reasoning with units and accuracy (N-Q). These standards sit in the Major Content and the Additional and Supporting Content categories, and several are fluency skills that show up on the calculator-prohibited Session 1a. Each dot-point page has its own practice: interpreting expressions, equivalent forms and factoring, polynomial operations, exponents and exponent rules, radicals and rational exponents, and units, quantities, and accuracy.

Reading the parts of an expression

An expression is built from terms (separated by $+$ or $-$), each a product of factors. A coefficient is the number multiplying a variable, and a constant is a term with no variable. In $3x^2 - 7x + 4$ the terms are $3x^2$, $-7x$, and $4$; the coefficient of $x$ is $-7$ (the sign travels with it). A-SSE.A.1 also asks you to read a grouped factor as one quantity: in $P(1 + 0.08)$ the factor $1.08$ means "the original plus 8 percent."

Factoring and equivalent forms

Two expressions are equivalent when they agree for every input; factoring rewrites a sum as a product.

To factor $x^2 + bx + c$, find two numbers that multiply to $c$ and add to $b$. Know the special patterns: difference of squares $a^2 - b^2 = (a + b)(a - b)$ and perfect-square trinomial $a^2 \pm 2ab + b^2 = (a \pm b)^2$. Factored form matters because it exposes the zeros.

Polynomial operations

Add and subtract by combining like terms, distributing a subtraction to every term. Multiply with the distributive property (FOIL for two binomials).

Polynomials are closed under add, subtract, and multiply: the result is always a polynomial.

Exponents and rational exponents

The exponent rules combine powers of the same base: $x^a x^b = x^{a+b}$ (add), $\frac{x^a}{x^b} = x^{a-b}$ (subtract), $(x^a)^b = x^{ab}$ (multiply), $x^0 = 1$, and $x^{-a} = \frac{1}{x^a}$. A rational exponent is a root: $x^{m/n} = \left(\sqrt[n]{x}\right)^m$, so $8^{2/3} = (\sqrt[3]{8})^2 = 4$. Put a square root in simplest radical form by removing the largest perfect-square factor: $\sqrt{50} = 5\sqrt{2}$.

Units and quantities

Use unit cancellation to convert and to check: write each conversion as a fraction so the unwanted unit cancels, leaving the unit you want. Choose units that fit the context, and report to an accuracy that matches the measurement, no more decimals than the data supports.

How this module is examined

• Equation response. Factor a quadratic, simplify a polynomial or exponential expression, or convert a rate.
• Multiple choice. Identify a coefficient, pick an equivalent form, or choose the most appropriately rounded answer.
• Session 1a (no calculator). Combining like terms, factoring, the exponent rules, and simplifying radicals are core no-calculator skills.

Check your knowledge

Work these as you would for credit on the online test.

1. In $-6x + 11$, name the coefficient of $x$ and the constant. (1 point)
2. Factor $x^2 + 7x + 12$. (2 points)
3. Factor $x^2 - 16$. (1 point)
4. Factor $3x^2 - 27$ completely. (2 points)
5. Simplify $(3x^2 + 5x - 2) - (x^2 - 4x + 6)$. (2 points)
6. Expand $(x + 5)(x - 3)$. (2 points)
7. Simplify $\dfrac{12x^5}{3x^2}$. (2 points)
8. Simplify $(2x^3)^2$. (1 point)
9. Evaluate $8^{2/3}$. (1 point)
10. Write $\sqrt{50}$ in simplest radical form. (2 points)