Question

say the answer with steps​

Answer 1

$\Large{\underbrace{\sf{\green{Required\:Solution:}}}}$

$\displaystyle{\bf{ 16a^{2}b^{2} - 8abc + c^{2}}}$

Sol'n. $\displaystyle{\sf{ 16a^{2}b^{2} - 8abc + c^{2}}}$

• Use identity (a-b)² = a² - 2ab + b² where a = 4ab and b = c and simplify.

$\longrightarrow{\sf{ (4ab)^{2} - 2 \times 4ab \times c + (c)^{2}}}$

$\longrightarrow{\sf{ (4ab-c)^{2}}}$

$\large\implies{\boxed{\sf{\green{ (4ab-c)(4ab-c)}}}}$

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Algebraic identity - An algebraic identity is an equality that holds for any values of its variables.

e.g.,

• (a+b)² = a² + 2ab + b²
• (a-b)² = a² - 2ab + b²
• a²-b² = (a-b)(a+b)
• a²+b² = (a+b)² - 2ab
• (x+a)(x+b) = x² + (a+b)x + ab
• (a+b)³ = a³ + b³ + 3ab(a+b)
• (a-b)³ = a³ - b³ - 3ab(a-b)
• a³+b³ = (a+b)³-3ab(a+b)

⠀⠀⠀⠀⠀⠀⠀= (a+b) (a²- ab + b²)

• a³-b³ = (a-b)³+3ab(a-b)

⠀⠀⠀⠀⠀⠀⠀= (a-b) (a² + ab + b²)

• (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca
• (a-b-c)² = a² + b² + c² - 2ab + 2bc - 2ca
• (a-b+c)² = a² + b² + c² - 2ab - 2bc + 2ca

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