General Strategy for Factoring Polynomials: exemplo 7.63

Problema e solução em inglês, como no livro original.

Factor completely: $4 a^{2} - 12 a b + 9 b^{2}$ .

Resolva no papel primeiro. Depois abra a solução um passo de cada vez e pare assim que conseguir terminar sozinho.

Sua vez

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Factor completely: $4 x^{2} + 20 x y + 25 y^{2}$ .

Como foi?

Is there a GCF?	No.
Is it a binomial, trinomial, or are there more terms?
Trinomial with $a \neq 1$ . But the first term is a perfect square.
Is the last term a perfect square?	Yes.
Does it fit the pattern, $a^{2} - 2 a b + b^{2} ?$	Yes.
Write it as a square.
Check your answer.
Is the expression factored completely?
Yes.
The binomial is not a difference of squares.
Multiply.
${(2 a - 3 b)}^{2}$
${(2 a)}^{2} - 2 \cdot 2 a \cdot 3 b + {(3 b)}^{2}$
$4 a^{2} - 12 a b + 9 b^{2} ✓$

Is there a GCF?	No.
Is it a binomial, trinomial, or are there more terms?
Trinomial with $a \neq 1$ . But the first term is a perfect square.
Is the last term a perfect square?	Yes.
Does it fit the pattern, $a^{2} - 2 a b + b^{2} ?$	Yes.
Write it as a square.
Check your answer.
Is the expression factored completely?
Yes.
The binomial is not a difference of squares.
Multiply.
${(2 a - 3 b)}^{2}$
${(2 a)}^{2} - 2 \cdot 2 a \cdot 3 b + {(3 b)}^{2}$
$4 a^{2} - 12 a b + 9 b^{2} ✓$