Algebraically prove that a-b2-a2-b2-2 a b

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Polynomial Expressions

Algebraically...

Question

Algebraically prove that

(a+b)² = a²+b²+2ab

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Solution

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

sin α = \frac{a^{2} - b^{2}}{a^{2} + b^{2}}

cot α = \frac{2 a b}{a^{2} - b^{2}}

L . H . S = R . H . S

(A + B)^{2} = A^{2} + B^{2} + 2 A B

Prove the following identities :

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

$(i i) (a - b)^{2} = a^{2} + b^{2} - 2 a b$ [2 MARKS]

(a^{2} - b^{2}) sin θ + 2 a b cos θ = a^{2} + b^{2}

tan θ = \frac{a^{2} - b^{2}}{2 a b}

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