Factories using suitable identities a) 16x²+24x+9 b)4p²x²+4px+1 c)49x²+98x+49 d)3p³+24p²+48p e)16k²-72kt+81t² f)m²x²+2mxy+x²y²
Answers
Step-by-step explanation:
Solution :-
a) Given that 16x²+24x+9
=> 4²x² +24x+3²
=> (4x)² + 2(4x)(3)+(3)²
=> (4x+3)²
=> (4x+3)(4x+3)
By (a+b)² = a²+2ab+b²
16x²+24x+9 = (4x+3)(4x+3)
b) Given that 4p²x²+4px+1
=> 2²p²x²+4px+1²
=> (2px)²+2(px)(2)+1²
=> (2px+1)²
=> (2px+1)(2px+1)
By (a+b)² = a²+2ab+b²
4p²x²+4px+1 = (2px+1)(2px+1)
c) Given that 49x²+98x+49
=> 7²x²+98x+7²
=> (7x)²+2(7x)(7) +7²
=> (7x+7)²
=> (7x+7)(7x+7)
By (a+b)² = a²+2ab+b²
49x²+98x+49 = (7x+7)(7x+7)
d) Given that 3p³+24p²+48p
=> 3p(p²+8p+16)
=> 3p(p²+2(p)(4)+4²)
=> 3p(p+4)²
=> 3p(p+4)(p+4)
By (a+b)² = a²+2ab+b²
3p³+24p²+48p = 3p(p+4)(p+4)
e) Given that 16k²-72kt+81t²
=> 81t²-72kt+16k²
=> (9t)²-2(9t)(4k)+(4k)²
=> (9t-4k)²
=> (9t-4k)(9t-4k)
By (a-b)² = a²-2ab+b²
16k²-72kt+81t² = (9t-4k)(9t-4k)
f) Given that m²x²+2mx²y+x²y²
=> (mx)²+2(mx)(xy)+(xy)²
=> (mx+xy)²
=> (mx+xy)(mx+xy)
=> (m+y)(m+y)(x²)
By (a+b)² = a²+2ab+b²
m²x²+2mx²y+x²y² = (m+y)(m+y)(x²)
Used Identities:-
→ (a+b)² = a²+2ab+b²
→ (a-b)² = a²-2ab+b²