Simplify (i) (x2 - 5) (x + 5) + 25 (ii) (a2 + 5)(b3 + 3) + 5 (iii) (t + s2) (t 2 - s) (iv) (a + b)(c - d) + (a - b)(c+ d ) + 2(ac + bd) (v) (x + y )(2x + y) + (x + 2y)(x - y) (vi) (x + y)(x2 - xy + y2) (vii) (1.5x - 4y)(1.5x + 4y + 3) - 4.5x + 12y (viii) (a + b + c)(a + b - c)

The simplified expressions for the following expressions (i) (x2 - 5) (x + 5) + 25 (ii) (a2 + 5)(b3 + 3) + 5 (iii) (t + s2) (t 2 - s) (iv) (a + b)(c - d) + (a - b)(c+ d ) + 2(ac + bd) (v) (x + y )(2x + y) + (x + 2y)(x - y) (vi) (x + y)(x2 - xy + y2) (vii) (1.5x - 4y)(1.5x + 4y + 3) - 4.5x + 12y (viii) (a + b + c)(a + b - c) are i) x3 + 5x2 - 5x ii) a2b3 + 3a2 + 5b3 + 20 iii) t3 - st + s2t 2 - s3 iv) 4ac v) 3x2 - y2 + 4xy vi) x3 + y3 vii) 2.25x2 - 16y2 viii) a2 + b2 - c2 + 2ab

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Simplify
(i) (x² - 5) (x + 5) + 25 (ii) (a² + 5)(b³ + 3) + 5
(iii) (t + s²) (t ² - s) (iv) (a + b)(c - d) + (a - b)(c+ d ) + 2(ac + bd)
(v) (x + y )(2x + y) + (x + 2y)(x - y) (vi) (x + y)(x²- xy + y²)
(vii) (1.5x - 4y)(1.5x + 4y + 3) - 4.5x + 12y
(viii) (a + b + c)(a + b - c)

Solution:

(i) (x² - 5)(x + 5) + 25

= x²(x + 5) - 5(x + 5) + 25

= x³ + 5x² - 5x - 25 + 25

= x³ + 5x² - 5x

(ii) (a² + 5)(b³ + 3) + 5

= a²(b³ + 3) + 5(b³ + 3) + 5

= a²b³ + 3a² + 5b³ + 15 + 5

= a²b³ + 3a² + 5b³ + 20

(iii) (t + s²)(t ² - s)

= t(t ² - s) + s²(t ² - s)

= t³ - st + s²t ² - s³

(iv) (a + b)(c - d) + (a - b)(c + d) + 2(ac + bd)

= a(c - d) + b(c - d) + a(c + d) - b(c + d) + 2(ac + bd)

= ac - ad + bc - bd + ac + ad - bc - bd + 2ac + 2bd

= (ac + ac + 2ac) + (ad - ad) + (bc - bc) + (2bd - bd - bd)

= 4ac

(v) (x + y)(2x + y) + (x + 2y)(x - y)

= x(2x + y) + y(2x + y) + x(x - y) + 2y(x - y)

= 2x² + xy + 2xy + y² + x² - xy + 2xy - 2y²

= (2x² + x²) + (y² - 2y²) + (xy + 2xy - xy + 2xy)

= 3x² - y² + 4xy

(vi) (x + y)(x² - xy + y²)

= x(x² - xy + y²) + y(x² - xy + y² )

= x³ - x²y + xy² + x²y - xy² + y³

= x³ + y³ + (xy² - xy²) + (x²y - x²y)

= x³ + y³

(vii) (1.5x - 4 y)(1.5x + 4y + 3) - 4.5x + 12 y

= 1.5x(1.5x + 4y + 3) - 4y(1.5x + 4y + 3) - 4.5x + 12y

= 2.25 x² + 6xy + 4.5x - 6xy - 16y² -12y - 4.5x + 12y

= 2.25x² + (6xy - 6xy) + (4.5x - 4.5x) - 16y² + (12y -12y)

= 2.25x² - 16y²

(viii) (a + b + c)(a + b - c)

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

= a² + ab - ac + ab + b² - bc + ca + bc - c²

= a² + b² - c² + (ab + ab) + (bc - bc) + (ca - ca)

= a² + b² - c² + 2ab

The simplified expressions are i) x³ + 5x² - 5x ii) a²b³ + 3a² + 5b³ + 20 iii) t³ - st + s²t ² - s³ iv) 4ac v) 3x² - y² + 4xy vi) x³ + y³ vii) 2.25x² - 16y² viii) a² + b² - c² + 2ab

☛ Check: NCERT Solutions for Class 8 Maths Chapter 9

Video Solution:

Simplify (i) (x² - 5) (x + 5) + 25 (ii) (a² + 5)(b³ + 3) + 5 (iii) (t + s²) (t ² - s) (iv) (a + b)(c - d) + (a - b)(c+ d ) + 2(ac + bd) (v) (x + y )(2x + y) + (x + 2y)(x - y) (vi) (x + y)(x²- xy + y²) (vii) (1.5x - 4y)(1.5x + 4y + 3) - 4.5x + 12y (viii) (a + b + c)(a + b - c)

NCERT Solutions Class 8 Maths Chapter 9 Exercise 9.4 Question 3

Summary:

The simplified expressions for the following expressions (i) (x² - 5) (x + 5) + 25 (ii) (a² + 5)(b³ + 3) + 5 (iii) (t + s²) (t ² - s) (iv) (a + b)(c - d) + (a - b)(c+ d ) + 2(ac + bd) (v) (x + y )(2x + y) + (x + 2y)(x - y) (vi) (x + y)(x²- xy + y²) (vii) (1.5x - 4y)(1.5x + 4y + 3) - 4.5x + 12y (viii) (a + b + c)(a + b - c) are i) x³ + 5x² - 5x ii) a²b³ + 3a² + 5b³ + 20 iii) t³ - st + s²t ² - s³ iv) 4ac v) 3x² - y² + 4xy vi) x³ + y³ vii) 2.25x² - 16y² viii) a² + b² - c² + 2ab

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