Question

what is the expansion of (p+q+3)^2​

Answer 1

(p+q+3)^2

= [(p+q)+3 ]^2

= (p+q)^2 + 2. (p + q).3 + (3)^2

= p^2+2pq+q^2 +6p+6q + 9

hope my answer helps you!

Answer 2

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what is the expansion of (p+q+3)^2

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Here,this identity is used:

$\bold{\boxed{ {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca}}$

$= > {(p + q + 3)}^{2} = {p}^{2} + {q}^{2} + {3}^{2} + 2(p)(q) + 2(q)(3) + 2(3)(p)$

$= {p}^{2} + {q}^{2} + 9 + 2pq + 6q + 6p$

$\bold{\red{= {p}^{2} + {q}^{2} + 2pq + 3(2p + 2q + 3)}}$

Other Related Formulas:

$\bold{\boxed{{(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab}}$

$\bold{\boxed{{(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b)}}$

$\bold{\boxed{{(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab}}$

$\bold{\boxed{{(a - b)}^{3} = {a}^{3} + {b}^{3} - 3ab(a - b)}}$

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