Question

-5x^2+30x-45=? 2y^4+54y=? 3xy^2-147x^3=?

Answer 1

-5х^2+30-45=-5(х^2-6х+9)=-5(х-3)(х-3)= -5(х-3)^2

2y^4+54y=2у(у^3+27)=2у(у+3)(у^2-3у+9)

3ху^2-147х^3=3х(у^2-49х^2)=3х(у-7х)(у+7х)

Answer 2

To simplify the expressions you provided, I'll go through each one separately:

1. -5x^2 + 30x - 45: To simplify this expression, we can factor out a common factor of -5: -5(x^2 - 6x + 9) Then, we can further simplify by factoring the quadratic expression inside the parentheses: -5(x - 3)^2 So the simplified form is -5(x - 3)^2.

2. 2y^4 + 54y: In this expression, there is no common factor to factor out. So, we cannot simplify it further. The simplified form remains as 2y^4 + 54y.

3. 3xy^2 - 147x^3: Here, we can factor out a common factor of 3x: 3x(y^2 - 49x^2) Now, we notice that the expression inside the parentheses is the difference of squares, so we can further simplify: 3x(y - 7x)(y + 7x) Thus, the simplified form is 3x(y - 7x)(y + 7x).

To summarize: -5x^2 + 30x - 45 simplifies to -5(x - 3)^2. 2y^4 + 54y remains as 2y^4 + 54y. 3xy^2 - 147x^3 simplifies to 3x(y - 7x)(y + 7x).