Quadratic Expansion

Algebra

Basic Concept
Video

Quadratic Expansion

$(a + b)^{2} = a^{2} + 2 a b + b^{2}$

$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 a c + 2 b c$

Example 01

Expand $(2 x + 5)^{2}$

$\begin{aligned} (2 x)^{2} + 2 . 2 x . 5 + 5^{2} \\ 4 x^{2} + 20 x + 25 \end{aligned}$

Example 02

Expand $(3 x - 4 y)^{2}$

$\begin{aligned} (3 x)^{2} - 2 . 3 x . 4 y + (4 y)^{2} \\ 9 x^{2} - 24 x y + 16 y^{2} \end{aligned}$

Example 03

Expand $(2 a + 3 b + c)^{2}$

$\begin{aligned} (2 a)^{2} + (3 b)^{2} + c^{2} + 2 . 2 a . 3 b + 2 . 2 a . c + 2 . 3 b . c \\ 4 a^{2} + 9 b^{2} + c^{2} + 12 a b + 4 a c + 6 b c \end{aligned}$

Example 04

Expand $(m - 2 n + 5 r)^{2}$

$\begin{aligned} m^{2} + (- 2 n)^{2} + (5 r)^{2} + 2 . m . - 2 n + 2 . m . 5 r + 2 . - 2 n . 5 r \\ m^{2} + 4 n^{2} + 25 r^{2} - 4 m n + 10 m r - 20 n r \end{aligned}$

Exercise

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