please answer all or 12 16 17 18 19
Answers
Answer:
Q12)=Here, The value of (3x+2y)^2 is 64.
Q13)=Here, The answer is 49x^2-9y^2-4z^2-12yz.
Q14)=Here, The value of x is (-1).
Q16)=In this question, The quotient is 2 and the remainder is (-3x).
Q17)=In this question, The qoutient is (x+5) and the remainder is 0.
Step-by-step explanation:
Q12.)=Here, As per our given question,
=3x-2y=4 -(1st)eq. ,
=xy=2 -(2nd)eq.
Now, 3x-2y=4
=3x=4+2y
=x=(4+2y)/3
By putting value of x in eq. 2,we get,
=(4+2y)/3×y=2
=(4y+2y^2)/3=2 (Y is multiplied to 4+2y)
=4y+2y^2=6
=2y+y^2=3 (As all numbers on both sides are divisible by 2)
=y^2+2y-3=0 [Standard form]
By solving the given equation by middle-term split method, we get,
=y^2-y+3y-3=0
=y(y-1)+3(y-1) (On taking common)
=(y+3) ,(y-1) (Again by taking common)
=y+3=0 ,y-1=0
=y=(-3) ,y=1
Now, By putting any one value of y in eq. 1,we get,
=3x-2(-3)=4
=3x+6=4
=3x=4-6
=3x=(-2)
=x=(-2)/3
Now, As per our question,
=(3x+2y)^2 (Here, identity=(a+b)^2=a^2+b^2+2ab)
=(3x)^2+(2y)^2+2×(3x)×(2y)
=[3×(-2/3)]-)^2+(2×(-3)^2+2×[3×(-2)/3)]×[2×(-3)]
=(-2)^2+36+2×(-2)×(-6)
=4+36+24
=64
So, Here, The value of (3x+2y)^2=64.
Thank you.
Q13.)=(a.)=49x^2-(3y+2z)^2
=(7x)^2-[(3y)^2+(2z)^2+2×(3y)×(2z)
=(7x)^2-[9y^2+4z^2+12yz]
=49x^2-9y^2-4z^2-12yz
So, It is the answer.
(b.)=(2ab+3xy) (2ab-3xy)
Here, The identity which is used:[(a+b) (a-b)=a^2-b^2]
So, by applying identity, we get,
=(2ab)^2-(3xy)^2
=4a^b^2 - 9x^2y^2
So, it is the answer.
Q14.)=[ (x+2) (2x-3) -2x^2+5]/2x+1=2
=[x(2x-3)+2(2x-3) -2x^2+5]/2x+1=2
=[(2x^2-3x)+(4x-6)-2x^2+5]/2x+1=2
=[2x^2-3x+4x-6-2x^2+5]/2x+1=2
=(x-1)/2x+1=2
Now, By cross-multiplying between both sides, we get,
=x-1=2(2x+1)
=4x+2-x+1=0
=3x+3=0
=3x=(-3)
=x=(-3)/3
=x=(-1)
So, Here, The value of x is (-1).
Q15.)=Complete question is not visible.
Q16.)=Here, As given in this question,
=p(x)=8x^2-2-3x ÷ g(x)=4x^2-1
=p(x)=8x^2-3x-2 [Standard form]
So,=(8x^2-3x-2)/4x^2-1
So, After division, we get,
=Our qoutient is=2, And remainder is=(-3x)
Now, Verification:
(Dividend=Divisor×Quotient+Remainder)
=8x^2-3x-2 =(4x^2-1)×(2)+(-3x)
=8x^2-2-3x
=8x^2-3x-2 (Verified).
Q17.)=Here, As in our question,
=p(x)=x^2-8x-65 ÷ g(x)=x-13
So,=(x^2-8x-65)/x-13
So, After division, we get,
=Our qoutient is=(x+5) and remainder is=0
So, Given polynomial is completely divisible by (x-13).
Thank you.