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Zorluk: KolayMultiplying Polynomials

The expression (2y−7)2(2y - 7)^2 is expanded into the standard polynomial form ay2+by+cay^2 + by + c. What is the value of the coefficient bb?

Cevap: -28

Cevap

-28
Expanding the perfect square binomial (2y−7)2(2y - 7)^2 requires multiplying (2y−7)(2y - 7) by itself. Using the distributive property, the outer product is (2y)(−7)=−14y(2y)(-7) = -14y and the inner product is (−7)(2y)=−14y(-7)(2y) = -14y. Combining these like terms gives a total middle term of −28y-28y. Because the required polynomial form is ay2+by+cay^2 + by + c, the value of the coefficient bb is exactly -28.

Adım Adım Çözüm

1
Rewrite the expression as a product of two binomials.
(2y−7)(2y−7)(2y - 7)(2y - 7)
Writing the binomial twice makes it easier to correctly apply the distributive property (FOIL method) and avoid missing the middle terms.
2
Distribute the terms.
4y2−14y−14y+494y^2 - 14y - 14y + 49
Multiplying the First terms, Outer terms, Inner terms, and Last terms ensures that every term in the first binomial is multiplied by every term in the second binomial.
3
Combine the like terms.
4y2−28y+494y^2 - 28y + 49
The middle terms, −14y-14y and −14y-14y, have the same variable raised to the same power, so their coefficients can be added together.
4
Identify the target coefficient.
−28-28
The standard polynomial form is given as ay2+by+cay^2 + by + c. The value of bb corresponds to the coefficient of the yy term.

Anahtar Kavram

Expanding Perfect Square Binomials
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Konular

Multiplying Polynomials

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