Question

☺ Solve it ☺

☺ Explanation Needed ☺.

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Answer 1

Given :

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

Solution :

• (2p + q + 5)²

Apply identity : (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac

→ (2p)² + (q)² + (5)² + 2*2p*q + 2*q*5 + 2*2p*5

→ 4p² + q² + 25 + 4pq + 10q + 20p

• (m + 2n + 3r)²

Apply identity : (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac

→ (m)² + (2n)² + (3r)² + 2*m*2n + 2*2n*3r + 2*m*3r

→ m² + 4n² + 9r² + 4mn + 12nr + 6mr

• (3x + 4y - 5p)²

Apply identity : (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac

→ (3x)² + (4y)² + (-5p)² + 2*3x*4y + 2*4y*(-5q) + 2*3x*(-5p)

→ 9x² + 16y² + 25p² + 24xy - 40yp - 30xp

• (7m - 3n - 4k)²

Apply identity : (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac

→ (7m)² + (-3n)² + (-4k)² + 2*7m*(-3n) + 2*(-3n)*(-4k) + 2*7m*(-4k)

→ 49m² + 9n² + 16k² - 42mn + 24nk - 56mk

Answer 2

QUESTION:-

✯.EXPAND.

✯(2p+q+5)²

✯(m+2n+3r)²

✯(3x+4y-5p)²

✯(7m-3n-4k)²

ANSWER✔

$\large\underline\bold{IDENTITY\:IN\:USE\:FOR\:THE\:EQUATIONS,}$

$\sf\large\dashrightarrow\bold (a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ac$

$\sf\star (2p+q+5)^2$

$\sf\implies (2p)^2+(q)^2+(5)^2+ 2 \times (2p) \times (q)+ 2 \times (q) \times (5)+2 \times (2p) \times (5)$

$\sf\implies 4p^2+q^2+25+4pq+10q+20p$

$\sf{\boxed{\bf{4p^2+q^2+25+4pq+10q+20p }}}$

$\sf\star (m+2n+3r)^2$

$\sf\implies (m)^2+(2n)^2+(3r)^2+ 2 \times (m) \times (2n)+ 2 \times (2n) \times (3r)+2 \times (m) \times (3r)$

$\sf\implies m^2+4n^2+9r^2+4mn+12nr+6mr$

$\sf{\boxed{\bf{m^2+4n^2+9r^2+4mn+12nr+6mr }}}$

$\sf\star (3x + 4y - 5p)^2$

$\sf\implies (3x)^2+(4y)^2+(-5p)^2+ 2 \times (3x) \times (4y)+ 2 \times (4y) \times (-5p)+2 \times (3x) \times (-5p)$

$\sf\implies 9x^2+16y^2+25p^2+24xy-40yp-30xp$

$\sf{\boxed{\bf{ 9x^2+16y^2+25p^2+24xy-40yp-30xp}}}$

$\sf\star (7m - 3n - 4k)^2$

$\sf\implies (7m)^2+(3n)^2+(4k)^2+ 2 \times (7m) \times (-3n)+ 2 \times (-3n) \times (-4k)+2 \times (7m) \times (-4k)$

$\sf\implies 49m^2+9n^2+16k^2-42mn+24nk-56mk$

$\sf{\boxed{\bf{ 49m^2+9n^2+16k^2-42mn+24nk-56mk}}}$

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