Show thati 3 x-72-84 x-3 x-72- ii 9 p-5 q2-180 p q-9 p-5 q2iii 4-3 m-3-4 n2-2 m n-16-9 m2-9-16 n2iv 4 p q-3 q2-4 p q-3 q2-48 p q2v a-ba-b-b-cb-c-c-ac-a-0

(i) L.H.S = (3x + 7)2 − 84x = (3x)2 + 2(3x)(7) + (7)2 − 84x = 9x2 + 42x + 49 − 84x = 9x2 − 42x + 49 R.H.S = (3x − 7)2 = (3x)2 − 2(3x)(7) +(7)2 = 9x2 − 42x + 49 ...

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Byju's Answer

Standard VIII

Mathematics

Addition and Subtraction of Algebraic Expression

Show thati 3 ...

Question

Show that

(i) (3x + 7)² − 84x = (3x − 7)²(ii) (9p − 5q)² + 180pq = (9p + 5q)²

(iii)

(iv) (4pq + 3q)²− (4pq − 3q)² = 48pq²

(v) (a − b) (a + b) + (b − c) (b + c) + (c − a) (c + a) = 0

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Solution

(i) L.H.S = (3x + 7)² − 84x

= (3x)² + 2(3x)(7) + (7)² − 84x

= 9x² + 42x + 49 − 84x

= 9x² − 42x + 49

R.H.S = (3x − 7)² = (3x)² − 2(3x)(7) +(7)²

= 9x²− 42x + 49

L.H.S = R.H.S

(ii) L.H.S = (9p − 5q)² + 180pq

= (9p)² − 2(9p)(5q) + (5q)² − 180pq

= 81p² − 90pq + 25q² + 180pq

= 81p² + 90pq + 25q²

R.H.S = (9p + 5q)²

= (9p)² + 2(9p)(5q) + (5q)²

= 81p² + 90pq + 25q²

L.H.S = R.H.S

(iii) L.H.S =

(iv) L.H.S = (4pq + 3q)²− (4pq − 3q)²

= (4pq)² + 2(4pq)(3q) + (3q)² − [(4pq)² − 2(4pq) (3q) + (3q)²]

= 16p²q² + 24pq² + 9q² − [16p²q² − 24pq² + 9q²]

= 16p²q² + 24pq² + 9q² −16p²q² + 24pq² − 9q²

= 48pq² = R.H.S

(v) L.H.S = (a − b) (a + b) + (b − c) (b + c) + (c − a) (c + a)

= (a² − b²) + (b² − c²) + (c² − a²) = 0 = R.H.S.

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Similar questions

Q. Show that:
(i)

(3 x + 7)^{2} - 84 x = (3 x - 7)^{2}

(ii)

(9 p - 5 q)^{2} + 180 p q = (9 p + 5 q)^{2}

(iii)

{(\frac{4}{3} m - \frac{3}{4} n)}^{2} + 2 m n = \frac{16}{9} m^{2} + \frac{9}{16} n^{2}

(iv)

(4 p q + 3 q)^{2} - (4 p q - 3 q)^{2} = 48 p q^{2}

(v)

(a - b) (a + b) + (b - c) (b + c) + (c - a) (c + a) = 0

Q. Show that:
(i) (3x + 7)² − 84x = (3x − 7)²
(ii) (9a − 5b)² + 180ab = (9a + 5b)²
(iii)

{(\frac{4 m}{3} - \frac{3 n}{4})}^{2} + 2 m n = \frac{16 m^{2}}{9} + \frac{9 n^{2}}{16}

(iv) (4pq + 3q)² − (4pq − 3q)² = 48pq²
(v) (a − b)(a + b) + (b − c)(b + c) + (c − a)( c + a) = 0

Q. Show that :

(i) {(3 x + 7)}^{2} - 84 x = {(3 x - 7)}^{2}

(i i) {(4 p q + 3 q)}^{2} - {(4 p q - 3 q)}^{2} = 48 p q^{2}

(i i i) (a - b) (a + b) + (b - c) (b + c) + (c - a) (c + a) = 0

Show that :

$(i) {(3 x + 7)}^{2} - 84 x = {(3 x - 7)}^{2}$

$(i i) {(4 p q + 3 q)}^{2} - {(4 p q - 3 q)}^{2} = 48 p q^{2}$

$(i i i) (a - b) (a + b) + (b - c) (b + c) + (c - a) (c + a) = 0$ [3 MARKS]

Q. Show that:

(9 p - 5 q)^{2} + 180 p q = (9 p + 5 q)^{2}

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Show that (i) (3x + 7)2 − 84x = (3x − 7)2 (ii) (9p − 5q)2 + 180pq = (9p + 5q)2 (iii) (iv) (4pq + 3q)2 − (4pq − 3q)2 = 48pq2 (v) (a − b) (a + b) + (b − c) (b + c) + (c − a) (c + a) = 0

Show that

(i) (3x + 7)² − 84x = (3x − 7)²(ii) (9p − 5q)² + 180pq = (9p + 5q)²

(iii)

(iv) (4pq + 3q)²− (4pq − 3q)² = 48pq²

(v) (a − b) (a + b) + (b − c) (b + c) + (c − a) (c + a) = 0