Question

Fill in the boxes with appropriate terms in the steps of expansion (4p-5q)² Solution: (4p-5q)² = (...) 2 (....) 5q + (...) = (...) 2(....) + (...)
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Answer 1

Answer:

i. (2p + q + 5)2 = (2p)2 + (q)2 + (5)2 + 2(2p) (q) + 2(q) (5) + 2(2p) (5) … [(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac] = 4p2 + q2 + 25 + 4pq + 10q + 20p ii. (m + 2n + 3r)2 = (m)2 + (2n)2 + (3r)2 + 2(m) (2n) + 2(2n) (3r) + 2(m) (3r) … [(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac] = m2 + 4n2 + 9r2 + 4mn + 12nr + 6mr iii. (3x + 4y – 5p)2 = (3x)2 + (4y)2 + (- 5p)2 + 2(3x) (4y) + 2(4y) (- 5p) + 2(3x) (- 5p) … [(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac] = 9x + 16y2 + 25p2 + 24xy – 40py – 30px iv. (7m – 3n – 4k)2 = (7m)2 + (- 3n)2 + (- 4k)2 + 2(7m) (- 3n) + 2 (- 3n) (- 4k) + 2 (7m) (- 4k) … [(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac] = 49m2 + 9n2 + 16k2 – 42mn + 24nk – 56km q-5-2-ii-m-2n-3r-2-iii-3x-4y-5p-2-iv-7m-3n-4k-2

Step-by-step explanation:

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Answer 2

i. (2p+q+5)2=(2p)2+(q)2+(5)2+2(2p ) (q)+2(q)(5)+2(2p)(5)...[(a+b+c)2=a2 +b2+c2+2ab+2bc+2ac]=4p2+q2+ 25+4pq+10q+20p ii.(m+2n+3r)2= (m)2+(2n)2+(3r)2+2(m)(2n)+2(2n)(3r) +2(m)(3r)...[(a+b+c)2=a2+b2+c2+ 2ab+2bc+2ac]=m2+4n2+9r2+4mn 12nr + 6mr iii. (3x+4y-5p)2=(3x)2+ (4y)2+(-5p)2+2(3x)(4y)+2(4y)(-5p)+ 2(3x)(-5p)...[(a+b+c)2=a2+b2+c2 +2ab+2bc+2ac]=9x+16y2+25p2+ 24xy-40py-30px iv.(7m-3n-4k)2= (7m)2+(-3n)2+(-4k)2+2(7m)(-3n)+2 (-3n)(-4k)+2(7m)(-4k)...[(a+b+c)2= a2+b2+c2+2ab+2bc+2ac]=49m2+ 9n2+16k2-42mn+24nk-56km q - 5 - 2 ii - m - 2n - 3r - 2 - iii - 3x - 4 iii - 3x - 4y - 5p - 2 - i iv-7m-3n- 4k-2