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Algebra 1

9.4.2 Rewrite Squared Expressions

Algebra 19.4.2 Rewrite Squared Expressions

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Activity

1. Write each expression in standard form:

(4x+1)2(4x+1)2

a. (5x2)2(5x2)2

b. (12x+7)2(12x+7)2

c. (3x+n)2(3x+n)2

d. (kx+m)2(kx+m)2

2. Decide if each expression is a perfect square. If so, write an equivalent expression of the form (kx+m)2(kx+m)2. If not, suggest one change to turn it into a perfect square.

a. 4x2+12x+94x2+12x+9

b. 4x2+8x+254x2+8x+25

Video: Rewrite Squared Expressions

Watch the following video to learn more about rewriting squared expressions.

Self Check

Find the equivalent factored expression for 4 x 2 + 12 x + 9 .
  1. ( 2 x + 3 ) ( 2 x 3 )
  2. ( 2 x + 3 ) 2
  3. ( 2 x 3 ) 2
  4. 4 ( x 2 + 3 x + 9 )

Factoring Perfect Square Trinomials

To factor perfect square trinomials, follow the formulas:

a2+2ab+b2=(a+b)2a2+2ab+b2=(a+b)2

a22ab+b2=(ab)2a22ab+b2=(ab)2

Let's look at an example of how to factor perfect square trinomials.

Example

Factor 9x2+12x+49x2+12x+4.

Step 1 - Does the trinomial fit the perfect square trinomial pattern, a2+2ab+b2a2+2ab+b2? If so, write the first term as a2a2 and last constant as b2b2.

  • Is the first term a perfect square? Write it as a square, a2a2. Is 9x29x2 a perfect square? Yes — write it as (3x)2(3x)2. 9x2+12x+4(3x)29x2+12x+4(3x)2
  • Is the last term a perfect square? Write it as a square, b2b2. Is 4 a perfect square? Yes — write it as (2)2(2)2. 9x2+12x+4(3x)2(2)29x2+12x+4(3x)2(2)2
  • Check the middle term. Is it 2ab2ab? Is 12x12x twice the product of 3x3x and 2? Does it match? Yes, so we have a perfect trinomial.

9x2+12x+4(3x)2(2)2(3x)2(2)22(3x)(2)12x9x2+12x+4(3x)2(2)2(3x)2(2)22(3x)(2)12x

Step 2 - Factor the binomial into: a2+2ab+b2=(a+b)2a2+2ab+b2=(a+b)2.

9x2+12x+49x2+12x+4

a2+2·a·b+b2(3x)2+2·3x·2+22(a+b)2(3x+2)2a2+2·a·b+b2(3x)2+2·3x·2+22(a+b)2(3x+2)2

Step 3 - Check.

(3x+2)2(3x+2)2

(3x)2+2·3x·2+22(3x)2+2·3x·2+22

9x2+12x+49x2+12x+4

Try it

Try It: Factoring Perfect Square Trinomials

Factor 9x230x+259x230x+25.

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