Question

activity
you already know how to solve quadratic equations by factoring and by using the quadratic formula. in this activity, you will use a new technique to rewrite and solve quadratic equations.
question 1
expand these expressions:
$(x + 3)^2$
$(x + a)^2$

Explanation:

Step1: Rewrite as product

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

Step2: Apply distributive property

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

Step3: Expand each term

$x(x+3)+3(x+3)=x^2+3x+3x+9$

Step4: Combine like terms

$x^2+3x+3x+9=x^2+6x+9$

Step5: Rewrite as product

$(x+a)^2=(x+a)(x+a)$

Step6: Apply distributive property

$(x+a)(x+a)=x(x+a)+a(x+a)$

Step7: Expand each term

$x(x+a)+a(x+a)=x^2+ax+ax+a^2$

Step8: Combine like terms

$x^2+ax+ax+a^2=x^2+2ax+a^2$

Answer:

$(x+3)^2 = x^2+6x+9$
$(x+a)^2 = x^2+2ax+a^2$