Are these Equivalent Expressions and Polynomials notes free?

Yes. The full 4-page Equivalent Expressions and Polynomials sheet is free inside CapCompass, which runs in your browser with no account needed.

What does the Equivalent Expressions and Polynomials revision sheet cover?

Equivalent means equal for every x, The patterns worth knowing cold, square of a sum, square of a difference, difference of two squares, product of two simple brackets, The calculator check for equivalence, Worked: subtracting one polynomial from another, Which factoring pattern is this, Why the factored form is the useful one, Rational expressions, one fraction rule at a time, Worked: simplifying a rational expression.

Is this for Digital SAT SAT Math?

Yes, it is written for the Digital SAT SAT Math syllabus.

🧭 CapCompassfree study planner

Equivalent Expressions and Polynomials — Digital SAT SAT Math revision notes

A 4-page visual revision sheet for Equivalent Expressions and Polynomials, written for Digital SAT SAT Math. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.

Equivalent Expressions and Polynomials revision notes, page 1 of 4 — Page 1 of 4. The remaining 3 pages open in the app.

Equivalent Expressions and Polynomials in one look

expand, factor, simplify, and prove two forms are the same thing

Equivalent means equal for every x

the question is nearly always which expression is equivalent to, and equivalent means the two forms agree for every legal value of x, not just for one
that gives you a shortcut the algebra does not: pick a number, put it into the original and into each option, and keep whichever option matches. Avoid 0 and 1, which make too many wrong options look right
the algebra itself is only four moves: distribute, collect like terms, factor, and cancel a common factor from top and bottom
these are grind questions rather than thinking questions, so they should come in under the 95 second average the 44-question, 70-minute Math section allows. Expanding a bracket is not where your time should go
no negative marking, so an expression you cannot simplify still gets an answer. Test x=2 in the original, test the options, and pick the one that agrees

The patterns worth knowing cold

square of a sum (a+b)^2=a^2+2ab+b^2
square of a difference (a-b)^2=a^2-2ab+b^2
difference of two squares a^2-b^2=(a-b)(a+b)
product of two simple brackets (x+p)(x+q)=x^2+(p+q)x+pq

Page 1 of 4. The full sheet, all 4 pages, opens free in the app.

What this Equivalent Expressions and Polynomials sheet covers

Equivalent means equal for every x
The patterns worth knowing cold
square of a sum
square of a difference
difference of two squares
product of two simple brackets
The calculator check for equivalence
Worked: subtracting one polynomial from another
Which factoring pattern is this
Why the factored form is the useful one
Rational expressions, one fraction rule at a time
Worked: simplifying a rational expression
The values that are not allowed
Worked: proving an option without doing the algebra
Traps that cost points
Tricks that save time

Open the full Equivalent Expressions and Polynomials sheet →Free, works offline, no account needed. All 4 pages, plus a study plan built around your own exam dates.

How CapCompass uses this sheet

These notes are not a standalone PDF. CapCompass plans SAT Math chapter by chapter against your real exam dates and free hours, and when the plan reaches Equivalent Expressions and Polynomials the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.