Question

factor of a2x2+ (a2+b2)x+b2=0

Answer 1

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a2x2+x(a2+b2)+b2=0
=>a2x2+a2x+b2x+b2=0
=>a2x(x+1)+b2(x+1)=0
=>(a2x+b2)(x+1)=0

The factors are (a2x+b2)&(x+1)
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By @Strange

Answer 2

Factors of $\bf {a}^{2} {x}^{2} + ( {a}^{2} + {b}^{2} )x + {b}^{2} = 0$ are $\bf \red{(x + 1)( {a}^{2} x + {b}^{2} )}$.

Given:

• ${a}^{2} {x}^{2} + ( {a}^{2} + {b}^{2} )x + {b}^{2} = 0$

To find:

• Find the factors of equation.

Solution:

Step 1:

Open bracket to simplify the equation.

${a}^{2} {x}^{2} + {a}^{2} x + {b}^{2} x + {b}^{2} = 0$

Step 2:

Take common from the first two and last two terms.

${a}^{2} x(x + 1) + {b}^{2} (x + 1) = 0$

Step 3:

Take common (x+1) from both terms.

$(x + 1)( {a}^{2}x + {b}^{2} ) = 0$

Thus,

Factors are $\bf (x + 1)( {a}^{2} x + {b}^{2} )$.

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