y^4-10y^3+21y^2
y^2(y^2-10y+21)
that help?
y^2(y^2-10y+21)
y^2(y-7)(y-3)
To simplify the given expression, let's factor it.
Given expression: y^4 - 10y^3 + 21y^2
Step 1: Look for the greatest common factor (GCF) among the terms.
In this case, the terms have a common factor of y^2.
Expression after factoring out GCF: y^2(y^2 - 10y + 21)
Step 2: Factor the quadratic expression (y^2 - 10y + 21).
To factor the quadratic expression, we need to find two numbers that multiply to give 21 and add up to -10 (coefficient of y).
Factoring the quadratic expression, we find:
y^2 - 10y + 21 = (y - 3)(y - 7)
So, the fully factored expression is:
y^4 - 10y^3 + 21y^2 = y^2(y - 3)(y - 7)