Class 9 Exam > Class 9 Notes > RD Sharma Solutions for Class 9 Mathematics > RD Sharma Solutions -Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths
Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics PDF Download
Q 1 . 64a3+125b3+240a2b+300ab2
SOLUTION :
= (4a)3+(5b)3+3(4a)2(5b)+3(4a)(5b)2 [∵a3+b3+3a2b+3ab2=(a+b)3]
= (4a+5b)3
= (4a+5b)(4a+5b)(4a+5b)
∴ 64a3+125b3+240a2b+300ab2 = (4a+5b)(4a+5b)(4a+5b)
Q 2 . 125x3−27y3−225x2y+135xy2
SOLUTION :
= (5x)3−(3y)3−3(5x)2(3y)+3(5x)(3y)2 [∵a3−b3−3a2b+3ab2=(a−b)3]
=(5x−3y)3
=(5x−3y)(5x−3y)(5x−3y)
∴ 125x3−27y3−225x2y+135xy2 = (5x−3y)(5x−3y)(5x−3y)
Q 3 .
SOLUTION :
[∵x3+b3+3x2b+3xb2=(x+b)3]
Q 4 . 8x3+27y3+36x2y+54xy2
SOLUTION :
= (2x)3+(3y)3+3×(2x)2×3y+3×(2x)(3y)2
= (2x+3y)3 [ ∵ a³ + b³ + 3a²b + 3ab² = (a + b) ³]
=(2x+3y)(2x+3y)(2x+3y)
∴ 8x3+27y3+36x2y+54xy2 = (2x+3y)(2x+3y)(2x+3y)
Q 5 . a3−3a2b+3ab2−b3+8
SOLUTION :
= (a−b)3+23 [∵a3−b3−3a2b+3ab2=(a−b)3]
=(a−b+2)((a−b)2−(a−b)2+22) ∵[a3+b3=(a+b)(a2−ab+b2)]
=(a−b+2)(a2+b2−2ab−2(a−b)+4)
=(a−b+2)(a2+b2−2ab−2a+2b+4)
∴ a3−3a2b+3ab2−b3+8 = (a−b+2)(a2+b2−2ab−2a+2b+4)
Q 6 . x3+8y3+6x2y+12xy2
SOLUTION :
= (x)3+(2y)3+3×x2×2y+3×x×(2y)2
= (x+2y)3 [∵x3+y3+3x2y+3xy2=(x+y)3]
=(x+2y)(x+2y)(x+2y)
∴ x3+8y3+6x2y+12xy2 = (x+2y)(x+2y)(x+2y)
Q 7 . 8x3+y3+12x2y+6xy2
SOLUTION :
= (2x)3+(y)3+3×(2x)2×y+3(2x)×y2
= (2x+y)3 [∵a3+b3+3a2b+3ab2=(a+b)3]
=(2x+y)(2x+y)(2x+y)
∴ 8x3+y3+12x2y+6xy2 = (2x+y)(2x+y)(2x+y)
Q 8 . 8a3+27b3+36a2b+54ab2
SOLUTION :
= (2a)3+(3b)3+3×(2a)2×3b+3×2a×(3b)2
= (2a+3b)3 [∵a3+b3+3a2b+3ab2=(a+b)3]
=(2a+3b)(2a+3b)(2a+3b)
∴ 8a3+27b3+36a2b+54ab2 =(2a+3b)(2a+3b)(2a+3b)
Q 9 . 8a3−27b3−36a2b+54ab2
SOLUTION :
= (2a)3−(3b)3−3×(2a)2×3b+3×2a×(3b)2
= (2a–3b)3 [∵a3−b3−3a2b+3ab2=(a−b)3]
=(2a–3b)(2a–3b)(2a–3b)
∴ 8a3−27b3−36a2b+54ab2 =(2a–3b)(2a–3b)(2a–3b)
Q 10 . x3−12x(x−4)−64
SOLUTION :
= x3−12x2+48x−64
= x3−3×x2×4+3×42×x−43
= (x−4)3 [∵a3−b3−3a2b+3ab2=(a−b)3]
=(x−4)(x−4)(x−4)
∴ x3−12x(x−4)−64 =(x−4)(x−4)(x−4)
Q 11 . a3x3−3a2bx2+3ab2x−b3
SOLUTION :
= (ax)3−3(ax)2×b+3(ax)×b2−b3
= (ax−b)3 [∵a3−b3−3a2b+3ab2=(a−b)3]
=(ax−b)(ax−b)(ax−b)
∴ a3x3−3a2bx2+3ab2x−b3 =(ax−b)(ax−b)(ax−b)
The document Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics is a part of the Class 9 Course RD Sharma Solutions for Class 9 Mathematics.
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FAQs on Ex-5.3, Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions - RD Sharma Solutions for Class 9 Mathematics
| 1. What is factorization of algebraic expressions? |  |
Ans. Factorization of algebraic expressions involves breaking down an algebraic expression into its constituent factors. It helps in simplifying complex expressions and solving equations more easily.
| 2. How do you factorize an algebraic expression? | |
Ans. To factorize an algebraic expression, we look for common factors among the terms and then use various methods like taking out the common factor, using identities, or using specific factorization formulas to break down the expression into factors.
| 3. Why is factorization important in mathematics? | |
Ans. Factorization is important in mathematics as it helps in simplifying complex expressions, solving equations, finding common factors, and identifying patterns. It also plays a crucial role in many mathematical concepts like simplifying fractions, finding roots of quadratic equations, and solving problems related to algebraic identities.
| 4. Can you explain the difference between factorization and expansion of algebraic expressions? | |
Ans. Factorization and expansion are opposite operations. Factorization involves breaking down an expression into its factors, while expansion involves multiplying factors to get the original expression. Factorization simplifies an expression, whereas expansion expands it to its original form.
| 5. What are some common factorization formulas used in algebra? | |
Ans. Some common factorization formulas used in algebra include the difference of squares formula (a^2 - b^2 = (a + b)(a - b)), the perfect square trinomial formula (a^2 + 2ab + b^2 = (a + b)^2), and the difference of cubes formula (a^3 - b^3 = (a - b)(a^2 + ab + b^2)). These formulas help in factorizing specific types of algebraic expressions.
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