Which of the equations are true identities? A. (x-2y)^(2)=x^(2)-4xy+4y^(2) B. (m+1)^(2)-m^(2)=1 Choose 1 answer: (A) Only A (B) Only B (C) Both A and B (D) Neither A nor B

Analyze option A: Let's first analyze option A: (x-2y)^(2)=x^(2)-4xy+4y^(2) We will use the formula (a-b)^2 = a^2 - 2ab + b^2 to expand the left side of the equation.Expand (x-2y)^2: Expanding (x-2y)^2 using the formula: (x-2y)^2 = x^2 - 2*(x)*(2y) + (2y)^2 = x^2 - 4xy + 4y^2Compare expanded form with right side: Now let's compare the expanded form with the right side of the equation given in option A: Expanded form: x^2 - 4xy + 4y^2 Given form: x^2 - 4xy + 4y^2 Since both forms are identical, option A is a true identity.Analyze option B: Next, we analyze option B: (m+1)^(2)-m^(2)=1 We will expand (m+1)^2 and then subtract m^2 to see if the result equals 1.Expand (m+1)^2 and subtract m^2: Expanding (m+1)^2 using the formula (a+b)^2 = a^2 + 2ab + b^2: (m+1)^2 = m^2 + 2*m*1 + 1^2 = m^2 + 2m + 1Compare result with 1: Now we subtract m^2 from both sides of the expanded form: (m^2 + 2m + 1) - m^2 = 2m + 1 This does not equal 1, as the right side of the equation in option B suggests.Since the result of the expansion and subtraction in option B does not equal 1, option B is not a true identity.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which of the equations are true identities?
A.
(x-2y)^(2)=x^(2)-4xy+4y^(2)
B.
(m+1)^(2)-m^(2)=1
Choose 1 answer:
(A) Only A
(B) Only B
(C) Both A and B
(D) Neither A nor B

Which of the equations are true identities? $\newline$ A. $(x-2 y)^{2}=x^{2}-4 x y+4 y^{2}$ $\newline$ B. $(m+1)^{2}-m^{2}=1$ $\newline$ Choose $1$ answer: $\newline$ (A) Only A $\newline$ (B) Only B $\newline$ (C) Both $\mathrm{A}$ and $\mathrm{B}$ $\newline$ (D) Neither $\mathrm{A}$ nor $\mathrm{B}$

View step-by-step help

Home

Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. Which of the equations are true identities?

\newline

(x-2 y)^{2}=x^{2}-4 x y+4 y^{2}

\newline

(m+1)^{2}-m^{2}=1

\newline

Choose

1

answer:

\newline

(A) Only A

\newline

(B) Only B

\newline

\mathrm{A}

and

\mathrm{B}

\newline

(D) Neither

\mathrm{A}

nor

\mathrm{B}

Analyze option A: Let's first analyze option A: $\newline$ $(x-2y)^{2}=x^{2}-4xy+4y^{2}$ $\newline$ We will use the formula $(a-b)^2 = a^2 - 2ab + b^2$ to expand the left side of the equation.
Expand $(x-2y)^2$ : Expanding $(x-2y)^2$ using the formula: $\newline$ $(x-2y)^2 = x^2 - 2\cdot(x)\cdot(2y) + (2y)^2 = x^2 - 4xy + 4y^2$
Compare expanded form with right side: Now let's compare the expanded form with the right side of the equation given in option A: $\newline$ Expanded form: $x^2 - 4xy + 4y^2$ $\newline$ Given form: $x^2 - 4xy + 4y^2$ $\newline$ Since both forms are identical, option A is a true identity.
Analyze option B: Next, we analyze option B: $\newline$ $(m+1)^{2}-m^{2}=1$ $\newline$ We will expand $(m+1)^2$ and then subtract $m^2$ to see if the result equals $1$ .
Expand $(m+1)^2$ and subtract $m^2$ : Expanding $(m+1)^2$ using the formula $(a+b)^2 = a^2 + 2ab + b^2$ : $\newline$ $(m+1)^2 = m^2 + 2\cdot m\cdot 1 + 1^2$ $\newline$ $= m^2 + 2m + 1$
Compare result with $1$ : Now we subtract $m^2$ from both sides of the expanded form: $\newline$ $(m^2 + 2m + 1) - m^2 = 2m + 1$ $\newline$ This does not equal $1$ , as the right side of the equation in option B suggests.
Compare result with $1$ : Now we subtract $m^2$ from both sides of the expanded form: $\newline$ $(m^2 + 2m + 1) - m^2 = 2m + 1$ $\newline$ This does not equal $1$ , as the right side of the equation in option B suggests. Since the result of the expansion and subtraction in option B does not equal $1$ , option B is not a true identity.