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# If a + b = c, then a^2 + 2ab + b^2 =

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Math Expert
Joined: 02 Sep 2009
Posts: 59573
If a + b = c, then a^2 + 2ab + b^2 =  [#permalink]

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21 Nov 2019, 00:53
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95% (00:17) correct 5% (00:35) wrong based on 21 sessions

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If $$a + b = c$$, then $$a^2+2ab+b^2 =$$

A. $$2c$$

B. $$c(a-b)$$

C. $$(a-b)(a+b)$$

D. $$c^2$$

E. $$a+b$$

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Senior Manager
Joined: 13 Feb 2018
Posts: 480
GMAT 1: 640 Q48 V28
Re: If a + b = c, then a^2 + 2ab + b^2 =  [#permalink]

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21 Nov 2019, 01:10
The ABC of Algebra: $$(a+b)^2=a^2+b^2+2ab$$

a+b=c
Substitute c in $$(a+b)^2$$ expression to get $$c^2$$

IMO
Ans: D
Manager
Joined: 20 Aug 2017
Posts: 55
Re: If a + b = c, then a^2 + 2ab + b^2 =  [#permalink]

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21 Nov 2019, 01:17
Bunuel wrote:
If $$a + b = c$$, then $$a^2+2ab+b^2 =$$

A. $$2c$$

B. $$c(a-b)$$

C. $$(a-b)(a+b)$$

D. $$c^2$$

E. $$a+b$$

$$(a+b)^2$$ = $$a^2+2ab+b^2$$

a+ b = c
so $$c^2$$ = $$a^2+2ab+b^2$$

IMO - D
Target Test Prep Representative
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Posts: 8619
Location: United States (CA)
Re: If a + b = c, then a^2 + 2ab + b^2 =  [#permalink]

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24 Nov 2019, 19:07
Bunuel wrote:
If $$a + b = c$$, then $$a^2+2ab+b^2 =$$

A. $$2c$$

B. $$c(a-b)$$

C. $$(a-b)(a+b)$$

D. $$c^2$$

E. $$a+b$$

Squaring both sides of a + b = c, we have:

(a + b)^2 = c^2

a^2 + b^2 + 2ab = c^2

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Re: If a + b = c, then a^2 + 2ab + b^2 =   [#permalink] 24 Nov 2019, 19:07
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