Question

Show that: (i) (3x + 7)2 – 84x = (3x – 7)2 (ii) (9p – 5q)2 + 180pq = (9p + 5q)2​

Answer 1

Answer:

(i)(3x+7)2-84x=(3x-7)2

=(10x)2-84x

=82x=(3x- 7)2

=(4x)2.

(ii)(9p-5q) +180pq=(9p+5q)2

=(4p)2+180q

=(184pq)2(9p+5q)2

=(184pq)2+(14pq)2

=198pq2.

Answer 2

Step-by-step explanation:

$i) \: {(3x + 7)}^{2} - 84x = \: {(3x - 7)}^{2} \\ l.h.s =.| {(3x + 7)}^{2} - 84x \\ = 9 {x}^{2} + 42x + 49 - 84x \\ = 9 {x}^{2} - 42x + 49 \\ = {(3x)}^{2} - (2 \times 3x \times 7) + {7}^{2} \\ = {(3x - 7)}^{2} \\. )proved(. \\ \\ ii) \: {(9p + 5q)}^{2} - 180pq = {(9p - 5q)}^{2} \\ l.h.s = .| {(9p + 5q)}^{2} - 180pq \\ = 81 {p}^{2} + 90pq + 25 {q}^{2} - 180pq \\ = 81 {p}^{2} - 90pq + 25 {q}^{2} \\ = {(9p)}^{2} - (2 \times 9p \times 5q) + {(5q)}^{2} \\ = {(9p - 5q)}^{2} \\ ).proved.($