expanding binomials of form $(ax+b)^2$

Question

I am able to answer the question: $(3x-5)^2$ by writing it out as $(3x-5)(3x-5)$. However, I know binomials can be expanded like: $(a+b)^2 = a^2 + 2ab + b^2$ How would I translate this into my question?

I've expanded it as $3x^2 + 2\cdotp(3x\cdotp(-5^2)) + (-5^2) = 3x^2 + 2 \cdotp(-3x+25)-25 =3x^2-6x+25$

odd, considering I found it to be $9x^2 -30x +25$ the other way,

You have an erroneous square, $(a+b)^2 = a^2 + 2ab + b^2$, not $a^2 + 2ab^2 + b^2$. — Daniel Fischer, Sep 02 '13 at 21:03

score 2 · Answer 1 · answered Sep 02 '13 at 21:04

2

The expansion of $(a+b)^2$ is incorrect; it should be $$(a+b)^2=a^2+2ab+b^2.$$

Also, when you substitute $a=3x$ into $a^2$, it becomes $(3x)^2=9x^2$.

answered Sep 02 '13 at 21:04

Rebecca J. Stones

26,845

score 2 · Answer 2 · answered Sep 02 '13 at 21:05

2

$(3x-5)^{2}=(3x-5)(3x-5)=(3x)^{2}+2((3x)(-5))+(-5)^{2}$

Take $a=3x$ and $b=-5$

answered Sep 02 '13 at 21:05

user71352

13,038

expanding binomials of form $(ax+b)^2$

2 Answers2