Algebra Formulas  and techniques, Formulas and forms for Mathematics. Bulacan State University
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Algebra Formulas and techniques, Formulas and forms for Mathematics. Bulacan State University

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College Algebra Formulas and Rules

Standard Form (Linear)

����+ ���� = ��

Point-Slope Formula

�� − ���� = ��(�� − ����) Slope-Intercept Form

�� =����+ �� Slope Formula

�� = ���� − ���� ���� − ����

Distance Formula

�� = �(���� − ����)�� + (���� − ����)��

Midpoint Formula

� ���� + ���� ��

, ���� + ���� �� �

General Form (Quadratic)

������ + ����+ �� = �� ���� ��(��) = ������ + ����+ ��; ��(��) ≡ ��

Standard (Vertex) Form

��(��) = ��(�� − ��)�� + �� Quadratic Formula

�� = −��± √���� − ������

����

Vertex of a Parabola

(��,��) = � −�� ���� ,�� �

−�� ������ ���� �

−�� ���� , �� −

����

�����

Equation of a Circle

���� = (�� − ��)�� + (�� − ��)��

�� = �(�� − ��)�� + (�� − ��)�� r = radius, (h, k) = center of circle

Difference of Squares

(���� − ����) = (�� − ��)(��+ ��) Sum of Squares

���� + ����;���������� Perfect Square Trinomial

���� + ������+ ���� = (��+ ��)�� ���� − ������+ ���� = (�� − ��)��

Difference of Cubes

���� − ���� = (�� − ��)����� + ����+ �����

Sum of Cubes

���� + ���� = (�� + ��)����� − ����+ �����

Tip: Use S.O.A.P. to remember the signs in the Diff. and Sum of Cubes formulas—Same, Opposite, Always Positive.

���� = �� ���� = ����������.

��−�� = �� ����

�� ≠ ��

� ����

����� ��

= ������

������

�� ≠ ��

(����)�� = ������

(����)�� = ��������

����

���� = ����−�� �� ≠ 0

�������� = ����+��

√�� �� = ����/��; n ≠ �� �√���� �

�� = √���� �� = ����/��

���� + ���� = ������ ������ − ���� = ���� �

�� ��

= √��

��� ; �� ≠ ��

���������� = �� ��log���� = ��

�� = log���� ⟺ ���� = �� ���������� = ��;

���������� = ����������.

������������ = ��

������������ = �� ����������

���������� = ���������� → �� = ��

���������� = ���������� ����������

Tip: Use the change of base formula to

convert to base 10 (log) or base e (ln). Some calculators handle only these bases.

������������ = ����������+ ����������

�������� �� �� = ���������� − ����������

LSC-O Learning Center (409) 882-3373 Ron E. Lewis Library building, rm. 113

Find this and other math resources on the LSC-O Learning Center Math Tutorials page.

http://www.lsco.edu/learningcenter/math.asp

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