can someone solve alll diz 10 sums & send an photo please.. thanks atons to them
Answers
Identity Rules :
• (a - b)² = a² - 2ab + b²
• (a + b)² = a² + 2ab + b²
• a² - b² = (a + b) (a - b)
Solutions :
i) Now, 80 - 5a²
= 5 (16 - a²)
= 5 (4² - a²)
= 5 (4 + a) (4 - a) ,
which is the required factorization.
ii) Now, x² - 4x + 4y - y²
= x² - y² - 4x + 4y
= (x + y) (x - y) - 4 (x - y)
= (x - y) (x + y - 4) ,
which is the required factorization.
iii) Now, 4x³ - 24x² + 36x
= 4x (x² - 6x + 9)
= 4x {x² - (2 * x * 3) + 3²}
= 4x (x - 3)²
= 4x (x - 3) (x - 3) ,
which is the required factorization.
iv) Now, (xy)⁴ - z⁴
= {(xy)²}² - (z²)²
= {(xy)² + z²} {(xy)² - z²}
= (x²y² + z²) (xy + z) (xy - z) ,
which is the required factorization.
v) Now, 15a (2p - 3q) - 10b (2p - 3q)
= (2p - 3q) (15a - 10b) ,
which is the required factorization.
vi) Now, 4x² - 10xy - 6xz + 15yz
= 4x² - 6xz - 10xy + 15yz
= 2x (2x - 3z) - 5y (2x - 3z)
= (2x - 3z) (2x - 5y) ,
which is the required factorization.
vii) Now, x² - 8x + 7
= x² - 7x - x + 7
= x (x - 7) - 1 (x - 7)
= (x - 7) (x - 1) ,
which is the required factorization.
viii) Now, 6x² - 7x - 20
= 6x² - 15x + 8x - 20
= 3x (2x - 5) + 4 (2x - 5)
= (2x - 5) (3x + 4) ,
which is the required factorization.
ix) Now, 2x² + 19xy + 24y²
= 2x² + 3xy + 16xy + 24y²
= x (2x + 3y) + 8y (2x + 3y)
= (2x + 3y) (x + 8y) ,
which is the required factorization.
x) Now, 3a² - 10a - 8
= 3a² - 4a - 6a - 8
= a (3a - 4) - 2 (3a - 4)
= (3a - 4) (a - 2) ,
which is the required factorization.
here is the answer....
Hope it helps....
