Question

how do you know that a given trinomial is a perfect square trinomial

Answer 1

Step-by-step explanation:

An expression obtained from the square of binomial equation is a perfect square trinomial. An expression is said to a perfect square trinomial if it takes the form ax2 + bx + c and satisfies the condition b2 = 4ac.

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Answer 2

By following the steps one can know that a given trinomial is a perfect square trinomial.

Step-by-step explanation:

• A perfect square trinomial is an expression derived from the square of a binomial equation. If an equation of the form $ax^{2} + bx + c$ and meets the requirement $b^{2} = 4ac$, it is said to be a perfect square trinomial.

The perfect square formula can be written as follows:

1. $(ax)^{2} + 2abx + b^{2} = (ax + b)^{2}$
2. $(ax)^{2}-2abx + b^{2} = (ax-b)^{2}$

• For example:

Factorize $x^{2} + 6x + 9$

Solution:

• We can rewrite the expression $x^{2} + 6x + 9$ in the form $a^{2} + 2ab + b^{2}$ as;

$(x)^{2} + 2 (x) (3) + (3)^{2}$

• Applying the formula $a^{2} + 2ab + b^{2} = (a + b)^{2}$ to the expression gives;

$=(x + 3)^{2}$

$=(x + 3) (x + 3)$