Perfect square trinomials are factored using the following standard form:
Given a2+2ab+b2 the factored form is --> (a+b)(a+b)=(a+b)2
Step 1. Verify that the first term and the third term are both perfect squares. (This means that the coefficients are perfect squares: 1, 4, 9, 16, 25... and that all the exponents of these two terms are even.)
Step 2. Verify that the middle term is twice the product of the square roots of the first and third term. (To square root a variable term with even exponents, you simply cut the given exponent in half.)
Step. 3. Use the standard form above to write the factored form.
Directions: Please factor the following.
4a2+20a+25
Step 1. Verify that the first term and the third term are both perfect squares.
4a2 --> The coefficient is a perfect square, 4, and the exponent of a2 is even. The square root of 4a2 is 2a.
25 --> This is a perfect square. The square root of 25 is 5.
Step 2. Verify that the middle term is twice the product of the square roots of the first and third term.
2a*5=10a
2(10a)=20a
20a is the middle term
Step 3. Use the standard form above to write the factored form.
(2a+5)(2a+5)
(2a+5)2
Directions: Please factor the following.
| 1. x2+6x+9 | 2. a2+10a+25 |
| 3. b2-4b+4 | 4. 9r2+42r+49 |
| 5. m2-20mb+100b2 | 6. 16y2+8y+1 |
| 7. 25b2-60bx+36x2 | 8. 64r2-16r+1 |
| 9. x2+2xy+y2 | 10. x2y4+xy2+y2 |
| 11. 100b4+140b2+49 | 12. 36+12b8+b16 |