Simplify using a table. Can someone help?

Mathematics

2 answers:

Alona [7]3 years ago

7 0

The product is -10y² -19y +15.

Fittoniya [83]3 years ago

5 0

Answer:

Option D. -10y² - 19y + 15

Step-by-step explanation:

we have to simplify the given expression

(-5y + 3)(2y + 5)

By distribution property

(-5y + 3)(2y + 5) = -5y(2y + 5) + 3(2y + 5)

= -10y²- 25y + 6y + 15

= -10y² - 19y + 15

Our answer matches with Option D.

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<h3>What is binomial theorem?</h3>

It provides algebraic expansion of exponentiated(integer) binomial.

According to binomial theorem,

$(a+b)^n = \sum_{i=0}^n ^nC_i a^ib^{n-i}$

<h3>How to use binomial theorem for given expression?</h3>

Taking a = x, and b =2y, we have n = 7, thus:

$(x+2y)^7 = \: ^7C_0x^0(2y)^7 + \: ^7C_1x^1(2y)^6 + \: ^7C_2x^2(2y)^5 + \: ^7C_3x^3(2y)^4 + \:^7C_4x^4(2y)^3 + \:^7C_5x^5(2y)^2 + \:^7C_6x^6y^1 + \: ^7C_0x^7y^0\\\\
(x+2y)^7 = 128y^7 + 448xy^6 + 672x^2y^5 + 560x^3y^4 + 280x^4y^3 + 84x^5y^2 + 14x^6y + x^7\\\\
(x+2y)^7 = x^7 + 14x^6y + 84x^5y^2 + 280x^4y^3 + 560x^3y^4 + 672x^2y^5 + 448xy^6 + 128y^7$