Kindly solve all the questions correctly step by step
Answers
Step-by-step explanation:
1 . evaluating:
(a) (y+3)^3
sol: (a+b)^3 = a^3+b^3 +3ab(a+b)
(y+3)^3 = y^3+3^3+3(y)(3)(y+3)
= y^3+27+9y^2+27y
= y^3+9y^2+27y+27
(b)(1001)^2
sol: (1000+1)^2
=(1000)^2 +(1)^2+2(1000)(1)
=1000000+1+2000
=1002001
(c)(a^2b^2-d^2)^2
sol:(a^2b^2-d^2)^2=(a^2b^2)^2+(d)^2-2(a^2b^2)(d^2)
=a^4b^4+d^4-2(a^2b^2d^2)
=a^4b^4+d^4-2a^2b^d^2
(d)97^2
sol: (97)^2=(100-3)^2
(100-3)^2=(100)^2+(3)^2-2(100)(3)
=10000+9-600
=9409
2.simplify 75×75+2×75×25+25×25
sol: 5625+3750+625
=10000
3.(a)(2x+3y+5z)^2
sol: (a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)
(2x+3y+5z)^2=(2x)^2+(3y)^2+(5z)^2+2[(2x)(3y)+(3y)(5z)+(2x)(5z)]
=4x^2+9y^2+25z^2+2(6xy+15yz+10xz)
=4x^2+9y^2+25z^2+12xy+30yz+20xz
(b)(k+2)^3
sol:(a+b)^3=a^3+b^3+3(ab)(a+b)
(k+2)^3=k^3+2^3+3(k)(2)(k+2)
=k^3+8+6k^2+12k
=k^3+6k^2+12k+8
(c)(106)^3
sol:(100+6)^3=(100)^3+(6)^3+3(100)(6)(100+6)
=10000+216+190800
=201016
(d)(996)^3
sol: (1000-4)^3=(1000)^3-(4)^3-3(1000)(4)(1000-4)
=1000000000-64-12000(996)
=988047936
4).sol:
a^3-b^3=(a-b)^3+3ab(a-b)
x-y=4
cubing on both sides
(x-y)^3 =64
x^3-y^3=(x-y)^3+3(xy)(x-y)
=64+3(21)(4)
=316
5).103^3+97^3
sol:103^3+97^3=(103+97)^3-3(103)(97)(103+97)
=(200)^3-3(9991)(200)
=8000000-5994600
=2005400
6).(4x-5y)(16x^2+20xy+25y^2)
sol:(4x-5y)[(4x)^2+(4x)(5y)+(5y)^2]
=(4x-5y)(4x+5y)^2
=(4x-5y)(4x+5y)(4x+5y)
(a-b)(a+b)=(a)^2-(b)^2
=(4x)^2-(5y)^2(4x+5y)
={(4x)^2}^2 - {(5y)^2}^2
=(4x)^4-(5y)^4
=256x^4-625y^4
I have answered your questions till 6th and I don't have time to answer others questions now I will answer later sorry