Question

express the following 16 minus p square minus Q square - 2 PQ​

Answer 1

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Express -:

$16 - {p}^{2} - {q}^{2} - 2pq$

$= 16 - ( {p}^{2} + {q}^{2} - 2pq)$

(Put the last three in a bracket by taking out minus(-) sign.

After taking out the minus sign the sign inside the brackets will also change.

$= {4}^{2} - ( {p}^{2} + {q}^{2} - 2 \times p \times q)$

$= {4}^{2} - (p - q)^{2}$

This expression is in the form of identity,

${a}^{2} - {b}^{2}$

So, its solution will be,

$(a + b)(a - b)$

So the answer to this question is -:

$(4 - p - q)(4 + p - q)$