Answer(4) 1:
128m^-2 / 3
.
Step-by-step explanation:
Given is (-4.m^2.n)^4 . ⅙.m^-10.n^-4 which needs to be written in a simpler form. We will divide the entire expression by the common denominator.
=256m^8n^4 .m^-10.n^-4 / 6
Making it in a more simpler form.
=128m^-2.n^0 / 3
=128m^-2.(1) / 3
=128m^-2 / 3
Hence the simplest form is 128m^-2 / 3
.
Answer (5) 2:
a^2 -14a-5
Step-by-step explanation:
Given expression is (8a^2 -6-8a) + (1-6a-7a^2)
Simplifying brackets
=8a^2 -6-8a+1-6a-7a^2
Rearranging the expression:
=8a^2 -7a^2 -8a-6a-6+1
=a^2 -14a-5
Hence the simplest form is a^2 -14a-5
Answer (6) 3:
-2x^3 -12x^2 +8x+6
Step-by-step explanation:
From the question, the expression is (6x-7x^2 +7) - (5x^2+2x-2x^3 -1)
Simplifying brackets:
=6x-7x^2 +7-5x^2 +2x-2x^3 -1
Rearranging the expression:
=-2x^3 -7x^2 -5x^2 +2x+6x+7-1
=-2x^3 -12x^2 +8x+6
Therefore, the simplest form is -2x^3 -12x^2 +8x+6
Answer(7) 4:
y^3 +10y^2 +50y+64
Step-by-step explanation:
Given is (y+4)^3 -2y(y-1)
As we know that: (a+b)^3 = a^3 +3(a^2)(b)+3(a)(b^2) +b^3
(y+4)^3 = y^3+3(y^2)(4)+3(y)(4^2)+4^3
(y+4)^3 =y^3 +12y^2 +48y^2 +64
=y^3 +12y^2 +48y +64-2y^2 +2y
Rearranging the expression:
=y^3 +12y^2 -2y^2 +48y+2y +64
=y^3 +10y^2 +50y+64
Therefore, the simplest form =y^3 +10y^2 +50y+64
Answer(8) 5:
3(k^3 -3k^2+9k-14)
Step-by-step explanation:
Give in the question is the expression (3k-6)(k^2-k+7)
=3k^3 -3k^2 +21k-6k^2 +6k-42
Rearranging the expression:
=3k^3 -3k^2-6k^2 +21k+6k-42
=3k^3 -9k^2 +27k -42
Factorizing 3 out of the equation:
=3(k^3 -3k^2+9k-14)
Therefore, the simplest form is 3(k^3 -3k^2+9k-14)
Answer(9) 6:
-(c^4.d^3-7c^2.d +3)
Step-by-step explanation:
Given in the question is the expression, -8c^6.d^4+56c^4.d^2-24c^2.d / 8c^2.d
Factorizing 8c^2.d out of the equation:
=8c^2.d(-c^4.d^3 +7c^2.d -3)
/8c^2.d
Divide 8c^2.d from numerator and denominator:
=-c^4.d^3 +7c^2.d -3
=-(c^4.d^3-7c^2.d +3)
Therefore, the simplest form is -(c^4.d^3-7c^2.d +3)
