#A02 · Algebra & Number Theory · Lv.1View in 3D Mind-Map

Polynomial Expansion & Factoring

Euclid & Diophantus · 300 BCE

(a+b)^2 = a^2 + 2ab + b^2,\quad a^2 - b^2 = (a-b)(a+b)

(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

Core algebraic identities governing polynomial expansion and factoring, enabling completing the square for quadratic solutions and series expansions.

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Term a

Term b

(5+3)^2 = 64.0, \quad 5^2 - 3^2 = 16.0

(a + b)² = a²+2ab+b²

64.00

a² - b² = (a-b)(a+b)

16.00

a³ + b³

152.00

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ax + b = 0 \implies x = -\frac{b}{a}

(a+b)^2 = a^2 + 2ab + b^2

가로·세로 길이가 (a+b)인 정사각형의 넓이는 a² 정사각형, b² 정사각형, 그리고 넓이가 ab인 직사각형 2개의 합과 정확히 같습니다.

Polynomial Kernel (SVM) feature expansion in ML and symbolic computer algebra systems

#Polynomial Kernel SVM#Symbolic Algebra#Completing Square

const sqSum = (a: number, b: number) => a*a + 2*a*b + b*b;