Question

Simplify (pqr) (pq³r) (p²r). Also, verify the result when p= -1 q= 2 r= -2​

Answer 1

GIVEN :-

• (pqr) (pq³r) (p²r)

TO FIND :-

• The value of (pqr) (pq³r) (p²r)
• Verify the results for p = -1 ,q = 2 ,r = -2

SOLUTION :-

⇒(pqr) (pq³r) (p²r)

⇒ [(pqr) (pq³r)] (p²r)

⇒(p²q⁴r²) (p²r)

⇒p⁴q⁴r³ = R.H.S

VERIFICATION :-

L.H.S = (pqr) (pq³r) (p²r)

= [(-1) × 2 × (-2)] [(-1) × (2)³ × (-2)] [(-1)² × (-2)]

= [-2 × -2 ] [-1 × -16] [ 1 × -2]

= 4 × 16 × (-2)

= -128 ----------------- (1)

R.H.S = p⁴q⁴r³

= (-1)⁴ × (2)⁴ × (-2)³

= 1 × 16 × (-8)

= -128 -------------------(2)

From equation (1) and (2)

L.H.S = R.H.S

HENCE VERIFIED

Answer 2

$\mathcal{\huge{\fbox{\purple{Solution:-}}}}$

✴ Simplification :-

(pqr) (pq³r) (p²r)

⇒(pqr) (pq³r) (p²r)

⇒ {(pqr)×(pq³r)}(p²r)

⇒(p²q⁴r²) (p²r)

⇒p⁴q⁴r³

▶ VERIFICATION :-

Left Hand Side

(pqr) (pq³r) (p²r)

➠ [(-1) × 2 × (-2)] [(-1) × (2)³ × (-2)] [(-1)² × (-2)]

➠ [-2 × -2 ] [-1 × -16] [ 1 × -2]

➠ 4 × 16 × (-2)

➠ 64 × -2

➠ -128

Right Hand Side

p⁴q⁴r³

➠ (-1)⁴ × (2)⁴ × (-2)³

➠ (-1 × -1 × -1 × -1 ) × (2×2×2×2) × (-2×-2×-2)

➠ 1 × 16 × (-8)

➠ 16 × -8

➠ -128

$\mathcal{\huge{\fbox{\red{L.H.S.=R.H.S}}}}$

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