Expand-1 2 p-q-522 m-2 n-3 r23 3 x-4 y-5 p24 7 m-3 n-4 k2

It is known that, a+b+c2=a2+b2+c2+2ab+2bc+2ca 1 #160;2p+q+52=2p2+q2+52+2 #215;2p #215;q+2 #215;q #215;5+2 #215;5 #215;2p=4p2+q2+25+4pq+10q+20p 2 ...

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Byju's Answer

Standard IX

Mathematics

(x±a)(x±b) = x²±(a+b)x+ab.

Expand.1 2 p+...

Question

Expand.
(1) (2p + q +5)²
(2) (m + 2n +3r)²
(3) (3x +4y − 5p)²
(4) (7m − 3n − 4k)²

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Solution

It is known that,
${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
$(1) {(2 p + q + 5)}^{2} = {(2 p)}^{2} + {(q)}^{2} + {(5)}^{2} + 2 \times 2 p \times q + 2 \times q \times 5 + 2 \times 5 \times 2 p = 4 p^{2} + q^{2} + 25 + 4 p q + 10 q + 20 p$
$(2) {(m + 2 n + 3 r)}^{2} = {(m)}^{2} + {(2 n)}^{2} + {(3 r)}^{2} + 2 \times m \times 2 n + 2 \times 2 n \times 3 r + 2 \times 3 r \times m = m^{2} + 4 n^{2} + 9 r^{2} + 4 m n + 12 n r + 6 m r$
$(3) {(3 x + 4 y - 5 p)}^{2} = {(3 x)}^{2} + {(4 y)}^{2} + {(- 5 p)}^{2} + 2 \times 3 x \times 4 y + 2 \times 4 y \times (- 5 p) + 2 \times (- 5 p) \times 3 x = 9 x^{2} + 16 y^{2} + 25 p^{2} + 24 x y - 40 y p - 30 p x$
$(4) {(7 m - 3 n - 4 k)}^{2} = {(7 m)}^{2} + (- 3 n^{2}) + {(- 4 k)}^{2} + 2 \times 7 m \times (- 3 n) + 2 \times (- 3 n) \times (- 4 k) + 2 \times (- 4 k) \times 7 m = 49 m^{2} + 9 n^{2} + 16 k^{2} - 42 m n + 24 n k - 56 k m$

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Expand. (1) (2p + q +5)2 (2) (m + 2n +3r)2 (3) (3x +4y − 5p)2 (4) (7m − 3n − 4k)2

Expand.
(1) (2p + q +5)²
(2) (m + 2n +3r)²
(3) (3x +4y − 5p)²
(4) (7m − 3n − 4k)²