Question

Show that :- (9p - 5q)² + 180pq = (9p + 5q)²

Answer 1

Answer:

Your answer is:-

Step by step explanation:

To prove

(9p - 5q)² + 180pq = (9p + 5q)²

proof

(9p−5q)² +180pq=(9p+5q)²

LHS➪(9p)² −2(9p)(5q)+(5q)² +180pq

➪81p² −90pq+25q² +180pq

➪81p² +90pq+25q²

RHS➪(9p+5q)²

➪(9p)² +2(9p)(5q)+(5q)²

➪81p² +90pq+25q²

LHS=RHS

Hence proved

Formula used

(a+b)²=a²+2ab+b²

(a-b)²=a²-2ab+b²

Answer 2

Given :-

• $(9p - 5q)² + 180pq = (9p + 5q)²$

Solution :-

$\implies LHS \: = (9p \: - \: 5q) {}^{2} \: + \: 180 \: pq$

$\implies (9p) {}^{2} \: - \: 2 \: \times \: 9p \: \times \: 5q \: + \: (5q) {}^{2} \: + \: 180pq$

$\implies(9p) {}^{2} \: - \: 90pq \: + \: (5q) {}^{2} \: + \: 180pq$

$\implies \: (9p) {}^{2} \: + \: 90pq \: + \: (5q) {}^{2}$

$\implies \: RHS \: = (9p \: + \: 5q) {)}^{2}$

$\implies \: LHS = RHS$