Find the following products:
(i) (3x+2y)(9x²-6xy+4y²)
(ii) (4x-5y)(16x²+20xy+25y²)
(iii) (7p⁴+q)(49p⁸-7p⁴q+q²)
(iv) (x/2 + 2y)(x²/4 - xy +4y²)
(v) (3/x - 5/y)(9/x² + 25/y² + 15/xy)
(vi) (3 + 5/x)(9 - 15/x + 25/x²)
(vii) (2/x + 3x)(4/x² + 9x² - 6)
(viii) (3/x - 2x²)(9/x² + 4x² - 6x)
(ix) (1+x)(1+x+x²)
(x) (1+x)(1-x+x²)
(xi) (x²-1)(x⁴+x²+1)
(xii)(x³+1)(x⁶-x³+1)
Answers
Concept :
By using an identity :
a³ + b³ = (a + b)(a² + b² - ab)
a³ - b³ = (a - b)(a² + b² + ab)
Given:
(i) (3x + 2y)(9x² - 6xy + 4y²)
= (3x + 2y)[(3x)²– (3x)(2y) + (2y)²)]
= (3x)³ + (2y)³
= 27x³ + 8y³
(ii) (4x - 5y)(16x² + 20xy + 25y²)
= (4x - 5y)[(4x)² + (4x)(5y) + (5y)²)]
= (4x)³ - (5y)³
= 64x³ - 125y³
(iii) (7p⁴ + q)(49p⁸ - 7p⁴q + q²)
= (7p⁴ + q)[(7p4)²– (7p⁴)(q) + (q)²)]
= (7p⁴)³ + (q)³
= 343p¹² + q³
(iv) (x/2 + 2y)(x²/4 - xy + 4y²)
= (x/2 + 2y) [(x/2)² – xy + (2y)²]
= (x/2)³ + (2y)³
= x³/8 + 8y³
(v) (3/x - 5/y)(9/x² + 25/y² + 15/xy)
= (3/x - 5/y)[(3/x)² + (5/y)² + 3/x × 5/y]
= (3/x)³ - (5/y)³
= 27/x³ - 125/y³
(vi) (3 + 5/x)(9 - 15/x + 25/x²)
= (3 + 5/x)[(3)² - 3 × 5/x + (5/x)²]
= 3³ + (5/x)³
= 27 + 125/x³
(vii) (2/x + 3x)(4/x² + 9x² - 6)
= (2/x + 3x)[(2/x)² + (3x)² - 2/x × 3x)
= (2/x)³ + (3x)³
= 8/x³ + 27x³
(viii) (3/x - 2x²)(9/x² + 4x² - 6x)
= (3/x - 2x²)[(3/x)² + (2x²)² - 3/x × 2x²)
= (3/x)³ - (2x²)³
= 27/x³ - 8x⁶
(ix) (1 + x)(1 + x + x²)
= (1 + x)[(1² + 1 × x + (x)²]
= (1)³ - (x)³
= 1 - x³
(x) (1 + x)(1- x + x²)
= (1 + x)[(1² - 1 × x + (x)²]
= (1)³ + (x)³
= 1 + x³
(xi) (x² -1)(x⁴ + x² + 1)
= (x² -1)[(x²)² + 1 × x² + 1²)
= (x²)³ - 1³
= x⁶ - 1
(xii)(x³ + 1)(x⁶- x³ + 1)
= (x³ + 1)[(x³)²- x³ × 1+ 1²)
= (x³)³ + 1³
= x⁹ + 1
HOPE THIS ANSWER WILL HELP YOU……
Some more questions :
If a+b=8 and ab=6, find the value of a³+b³.
https://brainly.in/question/15897806
Evaluate each of the following : (i) 111³-89³ (ii) 46³+34³ (iii) 104³+96³ (iv) 93³-107³
https://brainly.in/question/15897797
)x³ + 1)(x⁶- x³ + 1)
= (x³ + 1)[(x³)²- x³ × 1+ 1²)
= (x³)³ + 1³
= x⁹ + 1