Special Binomial Products

CCSS.MATH.CONTENT.HSA.APR.C.4

Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 - y2)2 + (2xy)2 can be used to generate Pythagorean triples.

CCSS.MATH.CONTENT.HSA.APR.C.5

Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.1

High School Algebra I

(10)  Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions. The student is expected to:

(A)  add and subtract polynomials of degree one and degree two;

(B)  multiply polynomials of degree one and degree two;

(C)  determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend;

(D)  rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property;

(E)  factor, if possible, trinomials with real factors in the form ax2 + bx + c, including perfect square trinomials of degree two; and

(F)  decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial.