Simplify-1 l-m-n2-l-m-n22 2 x-y-z2-2 x-y-z23 p-3 q-r2-p-3 q-r24 7 a-6 b-5 c2-7 a-6 b-5 c2

(1) (l + m + n)2 + (l ndash; m + n)2 =l2+m2+n2+2lm+2mn+2nl+l2+m2+n2 2lm 2mn+2nl=2l2+2n2+2m2+4nl (2)(2x + y + z)2 ndash; (2x + y ndash; z)2 =4x2+y2+z2+ ...

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Byju's Answer

Standard VIII

Mathematics

Addition and Subtraction of Algebraic Expression

Simplify:1 l+...

Question

Simplify:

(1) (l + m + n)² + (l – m + n)²
(2) (2x + y + z)² – (2x + y – z)²
(3) (p + 3q + r)² – (p – 3q + r)²
(4) (7a – 6b – 5c)² + (7a + 6b – 5c)²

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Solution

(1) (l + m + n)² + (l – m + n)²
$= (l^{2} + m^{2} + n^{2} + 2 l m + 2 m n + 2 n l) + (l^{2} + m^{2} + n^{2} - 2 l m - 2 m n + 2 n l) = 2 l^{2} + 2 n^{2} + 2 m^{2} + 4 n l$

(2)(2x + y + z)² – (2x + y – z)²
$= (4 x^{2} + y^{2} + z^{2} + 4 x y + 2 y z + 4 x z) - (4 x^{2} + y^{2} + z^{2} + 4 x y - 2 y z - 4 x z) = 4 x^{2} + y^{2} + z^{2} + 4 x y + 2 y z + 4 x z - 4 x^{2} - y^{2} - z^{2} - 4 x y + 2 y z + 4 x z = 4 y z + 8 x z$

(3) (p + 3q + r)² – (p – 3q + r)²
$= (p^{2} + 9 q^{2} + r^{2} + 6 p q + 6 q r + 2 r p) - (p^{2} + 9 q^{2} + r^{2} - 6 p q - 6 q r + 2 r p) = p^{2} + 9 q^{2} + r^{2} + 6 p q + 6 q r + 2 r p - p^{2} - 9 q^{2} - r^{2} + 6 p q + 6 q r - 2 r p = 12 p q + 12 q r$

(4) (7a – 6b – 5c)² + (7a + 6b – 5c)²
$= (49 a^{2} + 36 b^{2} + 25 c^{2} - 84 a b + 60 b c - 70 c a) + (49 a^{2} + 36 b^{2} + 25 c^{2} + 84 a b - 60 b c - 70 c a) = 98 a^{2} + 72 b^{2} + 50 c^{2} - 140 c a$

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Similar questions

Q. Simiplify:

(7 a - 6 b + 5 c)^{2} + (7 a + 6 b - 5 c)^{2}

Simplify: $(7 a - 6 b + 5 c)^{2}$

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(1) (x − 2y +3)² + (x + 2y − 3)²
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Q. Let image of the line

\frac{x - 1}{3} = \frac{y - 3}{5} = \frac{z - 4}{2}

in the plane

2 x - y + z + 3 = 0

L .

If a plane

7 x + p y + q z + r = 0

(p, q, r \in R)

is such that it contains the line

L

and perpendicular to the plane

2 x - y + z + 3 = 0,

then the value of

(p + 3 q + r)

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Simplify: (1) (l + m + n)2 + (l – m + n)2 (2) (2x + y + z)2 – (2x + y – z)2 (3) (p + 3q + r)2 – (p – 3q + r)2 (4) (7a – 6b – 5c)2 + (7a + 6b – 5c)2

Simplify:

(1) (l + m + n)² + (l – m + n)²
(2) (2x + y + z)² – (2x + y – z)²
(3) (p + 3q + r)² – (p – 3q + r)²
(4) (7a – 6b – 5c)² + (7a + 6b – 5c)²