Question

Calcula el cuadrado de cada binomio: A. (9 + 4m)^2

B. (X^10 - 5y^2)^2
C. (2x - 3z)^2
D. (4m^5 + 5n^3)^2
E. (3/6w - 1/2y)^2
F. (X10 - 5y2)2​

Answer 1

Part A)
`(9+4m)^(2)=81+72m+16m^(2)`

Part B)
`(x^(10)-5y^(2))^(2)=x^(20)-10x^(10)y^(2)+25y^(4)`

Part C)
`(2x-3z)^(2)=4x^(2)-12xz+9z^(2)`

Part D)
`(4m^(5)+5n^(3))^(2)=16m^(10)+40m^(5)n^(3)+25n^(6)`

Part E)
`((3)/(6)w-(1)/(2)y)^(2)=(9)/(36)w^(2)-(3)/(6)wy+(1)/(4)y^(2)`

Part F)
`(x^(10)-5y^(2))^(2)=x^(20)-10x^(10)y^(2)+25y^(4)`

Explanation:

The question in English is

Calculate the square of each binomial

we know that

The square of a binomial is always a trinomial

so

`(a+b)^(2)=a^(2)+2ab+b^(2)`

and

`(a-b)^(2)=a^(2)-2ab+b^(2)`

Part A) we have

`(9+4m)^(2)`

Applying the formula

`(9+4m)^(2)=(9)^(2)+2(9)(4m)+(4m)^(2)`

`(9+4m)^(2)=81+72m+16m^(2)`

Part B) we have

`(x^(10)-5y^(2))^(2)`

Applying the formula

`(x^(10)-5y^(2))^(2)=(x^(10))^(2)-2(x^(10))(5y^(2))+(5y^(2))^(2)`

`(x^(10)-5y^(2))^(2)=x^(20)-10x^(10)y^(2)+25y^(4)`

Part C) we have

`(2x-3z)^(2)`

Applying the formula

`(2x-3z)^(2)=(2x)^(2)-2(2x)(3z)+(3z)^(2)`

`(2x-3z)^(2)=4x^(2)-12xz+9z^(2)`

Part D) we have

`(4m^(5)+5n^(3))^(2)`

Applying the formula

`(4m^(5)+5n^(3))^(2)=(4m^(5))^(2)+2(4m^(5))(5n^(3))+(5n^(3))^(2)`

`(4m^(5)+5n^(3))^(2)=16m^(10)+40m^(5)n^(3)+25n^(6)`

Part E) we have

`((3)/(6)w-(1)/(2)y)^(2)`

Applying the formula

`((3)/(6)w-(1)/(2)y)^(2)=((3)/(6)w)^(2)-2((3)/(6)w)((1)/(2)y)+((1)/(2)y)^(2)`

`((3)/(6)w-(1)/(2)y)^(2)=(9)/(36)w^(2)-(3)/(6)wy+(1)/(4)y^(2)`

Part F) we have

`(x^(10)-5y^(2))^(2)`

Applying the formula

`(x^(10)-5y^(2))^(2)=(x^(10))^(2)-2(x^(10))(5y^(2))+(5y^(2))^(2)`

`(x^(10)-5y^(2))^(2)=x^(20)-10x^(10)y^(2)+25y^(4)`

Note the problem F is the same problem B