Simplify 3(x-2)^2/x-2
Is the answer 3x^2-10x+10?
If not then what is?
When p= sqrt2 and q= sqrt6 write pq in the form a(sqrt)b where a and b are integers and b is as small as possible.
Multiply out these brackets. Give your answer in the simplest form. (x+2y)(2x+y)
Is the answer 2x^2 + 2y^2 + 5xy?
If not then what is?
Also when there is an = sign but it is 3 lines instead of 2, what does this mean?
Thankyou xx
1) No as
3(x-2)^2/(x-2)=3(x-2)=3x-6
2) sqrt2 x sqrt 6 =sqrt(2x6)=sqrt12
=Sqrt(4x3) =sqrt4 x sqrt3 =2xsqrt3
therefore a is 2 and b is 3
3) yes you are correct
4) it means equivalent for all values of your variable ie no one unique answer it represents an identity
1) The given expression is (3(x-2)^2)/(x-2). To simplify this, we need to cancel out the (x-2) terms in the numerator and denominator.
Now, the expression becomes 3(x-2)/(1).
Simplifying further, we get 3(x-2) = 3x-6.
So, the correct answer is 3x-6, not 3x^2-10x+10.
2) Given p = √2 and q = √6, we need to find pq in the form a√b, where a and b are integers and b is as small as possible.
p√q = √2 × √6
√(2 × 6) = √12
Since 12 can be written as 4 × 3, the expression simplifies to √(4 × 3) = √4 × √3 = 2√3.
Therefore, pq = 2√3, where a = 2 and b = 3.
3) When multiplying out the brackets (x+2y)(2x+y), we need to use the distributive property.
(x+2y)(2x+y) = x(2x+y) + 2y(2x+y)
= (2x^2 + xy) + (4xy + y^2)
Combining like terms, we get 2x^2 + xy + 4xy + y^2.
Rearranging terms, the correct answer is 2x^2 + 5xy + y^2, not 2x^2 + 2y^2 + 5xy.
4) When an = sign has three lines instead of two, it represents an equivalence. It means that both sides of the equation are equal for all values of the variable. In other words, it represents an identity, indicating that the equation holds true regardless of the value of the variable.